pacman::p_load(tmap, sf, DT, stplanr,
performance, sp,
ggpubr, tidyverse, corrplot,
yardstick)Take-home Exercise 2: Applied Spatial Interaction Models: A case study of Singapore public bus commuter flows
1 Background
Urban commuters on the morning and traveling to work face complex mobility challenges, prompting questions about the impacts of public bus service removal along their routes. Traditional methods like commuter surveys are costly, time-consuming, and often result in outdated information. With the digitization of city-wide infrastructure and the widespread use of GPS on the vehicles and SMART cards in public transport, vast geospatial data sets are generated. However, the rapid growth of this data has overwhelmed planners, hindering their ability to transform it into meaningful insights and impacting the return on investment in data collection.
2 The Data
2.1 Open Government Data
For the purpose of this assignment, data from several open government sources will be used:
Passenger Volume by Origin Destination Bus Stops, Bus Stop Location, Train Station and Train Station Exit Point, just to name a few of them, from LTA DataMall.
Master Plan 2019 Subzone Boundary, HDB Property Information, School Directory and Information and other relevant data from Data.gov.sg.
hexagon, a hexagon layer of 375m (this distance is the perpendicular distance between the centre of the hexagon and its edges.) should be used to replace the relative coarse and irregular Master Plan 2019 Planning Sub-zone GIS data set of URA.
2.2 Specially collected data
Business, entertn, F&B, Leisure&Recreation are geospatial data sets of the locations of business establishments, entertainments, food and beverage outlets, leisure and recreation centres compiled for case study of Singapore public bus commuter flows. They are available on in the geospatial folder to Take-home Exercise 2 data folder.
HDB: This data set is the geocoded version of HDB Property Information data from data.gov. The data set is prepared using September 2021 data.
2 Getting Started
For the purpose of this study, 10 r packages will be used. They are:
tmap is a package for creating thematic maps. It provides a flexible and powerful framework for visualizing spatial data.
sf is an R package for simple features, which provides a standard way to encode spatial vector data.
DT is a package that extends the
data.tablepackage and provides functions to create interactive data tables in R Markdown documents and Shiny web applications.stplanr is a package for sustainable transport planning. It offers functions for transport planning and modeling, particularly with spatial data.
performance package is often associated with the
yardstickpackage and provides functions for model performance metrics, such as RMSE, MAE, etc.sp is a package for handling and analyzing spatial data. It is one of the foundational packages for spatial data manipulation and analysis in R.
ggpubr is a package for creating beautiful and customizable ggplot2-based plots for publication.
tidyverse is a collection of R packages, including
dplyr,ggplot2,tidyr, and others. It promotes a tidy data workflow and provides a consistent set of functions for data manipulation and visualization.corrplot is a package for visualizing correlation matrices using colored plots. It helps in understanding the relationships between variables in a dataset.
yardstick is a package for measuring model performance. It provides functions for computing various metrics, such as accuracy, precision, recall, and others.
The code chunk below installs and loads the various packages.
3 Data Preparation
3.1 Importing the OD data
Firstly, we will import the Passenger Volume by Origin Destination Bus Stops data set downloaded from LTA DataMall by using read_csv() of readr package.
Code
odbus <- read_csv("data/aspatial/origin_destination_bus_202308.csv",show_col_types = FALSE)Let use display the odbus tibble data table by using the code chunk below.
glimpse(odbus)Rows: 5,709,512
Columns: 7
$ YEAR_MONTH <chr> "2023-08", "2023-08", "2023-08", "2023-08", "2023-…
$ DAY_TYPE <chr> "WEEKDAY", "WEEKENDS/HOLIDAY", "WEEKENDS/HOLIDAY",…
$ TIME_PER_HOUR <dbl> 16, 16, 14, 14, 17, 17, 17, 17, 7, 17, 14, 10, 10,…
$ PT_TYPE <chr> "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "BUS", "…
$ ORIGIN_PT_CODE <chr> "04168", "04168", "80119", "80119", "44069", "4406…
$ DESTINATION_PT_CODE <chr> "10051", "10051", "90079", "90079", "17229", "1722…
$ TOTAL_TRIPS <dbl> 7, 2, 3, 10, 5, 4, 3, 22, 3, 3, 7, 1, 3, 1, 3, 1, …A quick check of odbus tibble data frame shows that the values in OROGIN_PT_CODE and DESTINATON_PT_CODE are in numeric data type. Hence, the code chunk below is used to convert these data values into character data type.
odbus$ORIGIN_PT_CODE <- as.factor(odbus$ORIGIN_PT_CODE)
odbus$DESTINATION_PT_CODE <- as.factor(odbus$DESTINATION_PT_CODE) 3.2 Extracting the study data
For this take home exercise, we will extract commuting flows on weekday and between 6 and 9 o’clock.
odbus6_9 <- odbus %>%
filter(DAY_TYPE == "WEEKDAY") %>%
filter(TIME_PER_HOUR >= 6 &
TIME_PER_HOUR <= 9) %>%
group_by(ORIGIN_PT_CODE,
DESTINATION_PT_CODE) %>%
summarise(TRIPS = sum(TOTAL_TRIPS))Table below shows the content of odbus6_9
Code
datatable(odbus6_9)4 Working with Geospatial Data
For the purpose of this exercise, three geospatial data will be used. They are:
Bus Stop Location from LTA DataMall. It provides information about all the bus stops currently being serviced by buses, including the bus stop code (identifier) and location coordinates.
MPSZ-2019: This data provides the sub-zone boundary of URA Master Plan 2019.
hexagon, a hexagon layer of 375m (this distance is the perpendicular distance between the centre of the hexagon and its edges.) should be used to replace the relative coarse and irregular Master Plan 2019 Planning Sub-zone GIS data set of URA.
4.1 Importing geospatial data
busstop <- st_read(dsn = "data/geospatial",
layer = "BusStop") %>%
st_transform(crs = 3414)Reading layer `BusStop' from data source
`C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 5161 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3970.122 ymin: 26482.1 xmax: 48284.56 ymax: 52983.82
Projected CRS: SVY21Let’s take a look at the location of bus stops in Singapore:
plot(busstop['BUS_STOP_N'])
mpsz <- st_read(dsn = "data/geospatial",
layer = "MPSZ-2019") %>%
st_transform(crs = 3414)Reading layer `MPSZ-2019' from data source
`C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 332 features and 6 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 103.6057 ymin: 1.158699 xmax: 104.0885 ymax: 1.470775
Geodetic CRS: WGS 84Let’s take a look at the map of subzone in Singapore.
Code
plot(mpsz['SUBZONE_C'])
4.2 Create Hexagon grid (honeycomb)
For this exercise purpose, we need to create an analytical hexagon data of 375m. (this distance is the perpendicular distance between the centre of the hexagon and its edges)
The following code creates a hexagon grid, associates bus stops with hexagons, and filters out hexagons without any bus stops. The resulting bs_num data frame contains information about hexagons with at least one bus stop.
area_honeycomb_grid = st_make_grid(busstop,cellsize = 750, what = "polygons", square = FALSE)
honeycomb_grid_sf = st_sf(area_honeycomb_grid) %>%
mutate(grid_id = 1:length(lengths(area_honeycomb_grid)))
honeycomb_grid_sf$num_bs = lengths(st_intersects(honeycomb_grid_sf, busstop))
bs_num = filter(honeycomb_grid_sf, num_bs > 0)Let’s take a look at the hexagon grid:
Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") +
tm_shape(bs_num) +
tm_fill("num_bs",alpha=0.8,palette = "Greens")+
tm_polygons()
5 Geospatial data wrangling
5.1 Combining Busstop and Hexagon grid
After running this code, honeycomb_grid will be a data frame containing information about bus stops that fall within the hexagons, including the bus stop ID (BUS_STOP_N), the hexagon ID (grid_id), and the number of bus stops within that hexagon (num_bs).
honeycomb_grid <- st_intersection(busstop, bs_num) %>%
select(BUS_STOP_N, grid_id,num_bs) %>%
st_drop_geometry()5.2 Combine odbus6_9 with od_data
For further visual operation, we need to combine a table contains the number of trips between pairs of origin and destination hexagons.
od_data <- left_join(odbus6_9, honeycomb_grid,
by = c("ORIGIN_PT_CODE" = "BUS_STOP_N")) %>%
rename(ORIGIN_BS = ORIGIN_PT_CODE,
ORIGIN_SZ = grid_id,
DESTIN_BS = DESTINATION_PT_CODE)Before continue, check for duplicating records.
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()Another left join between odbus6_9 and honeycomb_grid to get the DESTIN_BS.
od_data <- left_join(od_data, honeycomb_grid,
by = c("DESTIN_BS" = "BUS_STOP_N")) %>%
rename(DESTIN_SZ = grid_id)Before continue, check for duplicating records.
duplicate <- od_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()Group by ‘ORIGIN_GRID_ID’ and ‘DESTIN_GRID_ID’ to create a new column ‘MORNING_PEAK’ representing the total number of trips between each pair of hexagons.
od_data <- od_data %>%
drop_na() %>%
group_by(ORIGIN_SZ, DESTIN_SZ) %>%
summarise(MORNING_PEAK = sum(TRIPS))6 Visualising Spatial Interaction
6.1 Removing intra-zonal flows
We will not plot the intra-zonal flows. The code chunk below will be used to remove intra-zonal flows.
od_data1 <- od_data[od_data$ORIGIN_SZ!=od_data$DESTIN_SZ,]6.2 Create flowline
flowLine <- od2line(flow = od_data1,
zones = bs_num,
zone_code = "grid_id")6.3 Visualisation and Analysis
Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") +
tm_shape(bs_num) +
tm_fill("num_bs",alpha=0.8,palette = "Greens")+
tm_polygons() +
flowLine %>%
filter(MORNING_PEAK >= 5000) %>%
tm_shape() +
tm_lines(lwd = "MORNING_PEAK",
style = "quantile",
scale = c(0.3,3, 6, 9, 12, 18,21, 27),
n = 6,
alpha = 0.5,
col="yellow") +
tm_layout(main.title = 'OD Flow On Weekday Morning Peak hour' ,
main.title.position = "center",
main.title.size = 1,
main.title.fontface = 'bold') +
tm_compass(type="8star", size = 1) +
tm_scale_bar()
In this map, we filtered out trips with a count less than 5000 for enhanced analysis. Thicker flowlines indicate a higher volume of trips, while the length of the flowlines represents the distance between each hexagon. Notably, we observe long lines from the northern to the eastern regions, which, upon referencing the Singapore subway map, suggests a lack of subway connections along that route. Additionally, thicker lines predominantly appear in darker-colored hexagons, indicating a positive correlation between the number of bus stations and trip volume.
Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") +
tm_shape(bs_num %>%
filter(num_bs <= 3)) +
tm_fill("num_bs",alpha=0.8,palette = "Greens")+
tm_polygons() +
tm_shape(flowLine %>%
filter(MORNING_PEAK >= 20000)) +
tm_lines(lwd = "MORNING_PEAK",
style = "quantile",
scale = c(0.3,3, 6, 9, 12, 18,21, 27),
n = 6,
alpha = 0.5,
col="yellow") +
tm_layout(main.title = 'OD Flow On Weekday Morning Peak hour' ,
main.title.position = "center",
main.title.size = 1,
main.title.fontface = 'bold') +
tm_compass(type="8star", size = 1) +
tm_scale_bar()
After filtering for bus stops with a count of 3 or fewer and trips exceeding 20000, we observe a significant reduction in the overlap between flow lines and hexagons. This confirms the earlier understanding of the relationship between bus stations and trip volume. However, notable overlaps persist in the northern part of Singapore. Given the geographical context, this is likely attributed to buses traveling between Malaysia and Singapore—routes with fewer stations but higher trip volumes.
7 Assemble propulsive and attractiveness variables
business <- st_read(dsn = "data/geospatial",
layer = "Business") %>%
st_transform(crs = 3414)Reading layer `Business' from data source
`C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 6550 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 3669.148 ymin: 25408.41 xmax: 47034.83 ymax: 50148.54
Projected CRS: SVY21 / Singapore TMbs_num$`BUSINESS_num`<- lengths(
st_intersects(
bs_num, business))summary(bs_num$BUSINESS_num) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 0.000 1.000 7.273 7.000 97.000 Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") +
tm_shape(bs_num) +
tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(business) +
tm_dots(size = 0.05, col = "yellow") 
fb <- st_read(dsn = "data/geospatial", layer = "F&B") %>% st_transform(crs = 3414)Reading layer `F&B' from data source
`C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 1919 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6010.495 ymin: 25343.27 xmax: 45462.43 ymax: 48796.21
Projected CRS: SVY21 / Singapore TMbs_num$`FB_num`<- lengths(
st_intersects(
bs_num, fb))summary(bs_num$FB_num) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 0.000 0.000 2.204 1.000 133.000 Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") + tm_shape(bs_num) +
tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(fb) +
tm_dots(size = 0.05, col = "yellow") 
lr <- st_read(dsn = "data/geospatial",
layer = "Liesure&Recreation") %>%
st_transform(crs = 3414)Reading layer `Liesure&Recreation' from data source
`C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 1217 features and 30 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 6010.495 ymin: 25134.28 xmax: 48439.77 ymax: 50078.88
Projected CRS: SVY21 / Singapore TMbs_num$`lr_num`<- lengths(
st_intersects(
bs_num, lr))summary(bs_num$lr_num) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000 0.000 0.000 1.307 1.000 41.000 Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") + tm_shape(bs_num) +
tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(lr) +
tm_dots(size = 0.05, col = "yellow") 
schools <- read_csv("data/aspatial/schools.csv") %>%
rename(latitude = "results.LATITUDE",
longitude = "results.LONGITUDE")%>%
select(postal_code, school_name, latitude, longitude)schools_sf <- st_as_sf(schools,
coords = c("longitude", "latitude"),
crs=4326) %>%
st_transform(crs = 3414)bs_num$`schools_num`<- lengths(
st_intersects(
bs_num, schools_sf))summary(bs_num$schools_num) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.0000 0.0000 0.4125 1.0000 4.0000 Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") + tm_shape(bs_num) +
tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(schools_sf) +
tm_dots(size = 0.05, col = "yellow") 
hdb <- read_csv("data/aspatial/hdb.csv") %>%
rename(latitude = "lat",
longitude = "lng")hdb_sf <- st_as_sf(hdb,
coords = c("longitude", "latitude"),
crs=4326) %>%
st_transform(crs = 3414)bs_num$`hdb_num`<- lengths(
st_intersects(
bs_num, hdb_sf))summary(bs_num$hdb_num) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00 0.00 0.00 14.85 27.00 103.00 Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") + tm_shape(bs_num) +
tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(hdb_sf) +
tm_dots(size = 0.05, col = "yellow") 
entertn <- st_read(dsn = "data/geospatial",
layer = "entertn") %>%
st_transform(crs = 3414)Reading layer `entertn' from data source
`C:\cjh202311\isss624\Take-home_Ex\Take-home_Ex2\data\geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 114 features and 3 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 10809.34 ymin: 26528.63 xmax: 41600.62 ymax: 46375.77
Projected CRS: SVY21 / Singapore TMbs_num$`entertn_num`<- lengths(
st_intersects(
bs_num, entertn))summary(bs_num$entertn_num) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0000 0.0000 0.0000 0.1331 0.0000 9.0000 Code
tmap_mode("plot")
tmap_options(check.and.fix = TRUE)
tm_shape(mpsz) +
tm_borders(alpha=0.7,col = "white")+
tm_polygons("darkgrey") +
tm_shape(bs_num) +
tm_polygons(alpha=0.5, col = "darkgreen")+
tm_shape(entertn) +
tm_dots(size = 0.05, col = "yellow") 
The data will be joined with :
bs_num_tidy <- bs_num %>%
st_drop_geometry() %>%
select(grid_id, BUSINESS_num, FB_num, lr_num, schools_num, hdb_num, entertn_num )flow_data <- od_data1 %>%
left_join(bs_num_tidy,
by = c("DESTIN_SZ" = "grid_id"))Code
summary(flow_data) ORIGIN_SZ DESTIN_SZ MORNING_PEAK BUSINESS_num
Min. : 23 Min. : 23 Min. : 1.0 Min. : 0.000
1st Qu.:1099 1st Qu.:1116 1st Qu.: 7.0 1st Qu.: 0.000
Median :1433 Median :1432 Median : 38.0 Median : 1.000
Mean :1416 Mean :1414 Mean : 385.1 Mean : 7.302
3rd Qu.:1728 3rd Qu.:1711 3rd Qu.: 180.0 3rd Qu.: 6.000
Max. :2505 Max. :2505 Max. :96644.0 Max. :97.000
FB_num lr_num schools_num hdb_num
Min. : 0.000 Min. : 0.000 Min. :0.0000 Min. : 0.00
1st Qu.: 0.000 1st Qu.: 0.000 1st Qu.:0.0000 1st Qu.: 0.00
Median : 0.000 Median : 1.000 Median :0.0000 Median : 10.00
Mean : 5.776 Mean : 2.368 Mean :0.5291 Mean : 19.39
3rd Qu.: 2.000 3rd Qu.: 3.000 3rd Qu.:1.0000 3rd Qu.: 34.00
Max. :133.000 Max. :41.000 Max. :4.0000 Max. :103.00
entertn_num
Min. :0.000
1st Qu.:0.000
Median :0.000
Mean :0.336
3rd Qu.:0.000
Max. :9.000 We can see there are 0 values in BUSINESS_num, FB_num, lr_num, schools_num, hdb_num, entertn_num.
The code chunk below will be used to replace zero values to 0.99 for the propulsive and attractiveness variables.
flow_data$BUSINESS_num <- ifelse(
flow_data$BUSINESS_num == 0,
0.99, flow_data$BUSINESS_num)
flow_data$FB_num <- ifelse(
flow_data$FB_num == 0,
0.99, flow_data$FB_num)
flow_data$lr_num <- ifelse(
flow_data$lr_num == 0,
0.99, flow_data$lr_num)
flow_data$schools_num <- ifelse(
flow_data$schools_num == 0,
0.99, flow_data$schools_num)
flow_data$hdb_num <- ifelse(
flow_data$hdb_num == 0,
0.99, flow_data$hdb_num)
flow_data$entertn_num<- ifelse(
flow_data$entertn_num == 0,
0.99, flow_data$entertn_num)Code
summary(flow_data) ORIGIN_SZ DESTIN_SZ MORNING_PEAK BUSINESS_num
Min. : 23 Min. : 23 Min. : 1.0 Min. : 0.990
1st Qu.:1099 1st Qu.:1116 1st Qu.: 7.0 1st Qu.: 0.990
Median :1433 Median :1432 Median : 38.0 Median : 1.000
Mean :1416 Mean :1414 Mean : 385.1 Mean : 7.729
3rd Qu.:1728 3rd Qu.:1711 3rd Qu.: 180.0 3rd Qu.: 6.000
Max. :2505 Max. :2505 Max. :96644.0 Max. :97.000
FB_num lr_num schools_num hdb_num
Min. : 0.990 Min. : 0.990 Min. :0.990 Min. : 0.99
1st Qu.: 0.990 1st Qu.: 0.990 1st Qu.:0.990 1st Qu.: 0.99
Median : 0.990 Median : 1.000 Median :0.990 Median : 10.00
Mean : 6.306 Mean : 2.769 Mean :1.171 Mean : 19.76
3rd Qu.: 2.000 3rd Qu.: 3.000 3rd Qu.:1.000 3rd Qu.: 34.00
Max. :133.000 Max. :41.000 Max. :4.000 Max. :103.00
entertn_num
Min. :0.990
1st Qu.:0.990
Median :0.990
Mean :1.183
3rd Qu.:0.990
Max. :9.000 Now, there is no zero values in our data.
Next we will remove duplicate record:
duplicate <- flow_data %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()flow_data <- unique(flow_data)Code
summary(flow_data) ORIGIN_SZ DESTIN_SZ MORNING_PEAK BUSINESS_num
Min. : 23 Min. : 23 Min. : 1.0 Min. : 0.990
1st Qu.:1099 1st Qu.:1116 1st Qu.: 7.0 1st Qu.: 0.990
Median :1433 Median :1432 Median : 38.0 Median : 1.000
Mean :1416 Mean :1414 Mean : 385.1 Mean : 7.729
3rd Qu.:1728 3rd Qu.:1711 3rd Qu.: 180.0 3rd Qu.: 6.000
Max. :2505 Max. :2505 Max. :96644.0 Max. :97.000
FB_num lr_num schools_num hdb_num
Min. : 0.990 Min. : 0.990 Min. :0.990 Min. : 0.99
1st Qu.: 0.990 1st Qu.: 0.990 1st Qu.:0.990 1st Qu.: 0.99
Median : 0.990 Median : 1.000 Median :0.990 Median : 10.00
Mean : 6.306 Mean : 2.769 Mean :1.171 Mean : 19.76
3rd Qu.: 2.000 3rd Qu.: 3.000 3rd Qu.:1.000 3rd Qu.: 34.00
Max. :133.000 Max. :41.000 Max. :4.000 Max. :103.00
entertn_num
Min. :0.990
1st Qu.:0.990
Median :0.990
Mean :1.183
3rd Qu.:0.990
Max. :9.000 The following table is explanatory variables to be used in the Spatial Interaction Modelling:
| No | Explanatory Variables |
|---|---|
| 1 | Business |
| 2 | F&B |
| 3 | Leisure&Rrecreation |
| 4 | schools |
| 5 | HDB |
| 6 | Entertainment |
8 Compute Distance Matrix
8.1 Converting from sf data.table to SpatialPolygonsDataFrame
First as.Spatial() will be used to convert bs_num from sf tibble data frame to SpatialPolygonsDataFrame of sp object as shown in the code chunk below. Computing distance matrix using sp than sf package.
bs_num_sp <- as(bs_num, "Spatial")8.2 Computing the distance matrix
Next, spDists() of sp package will be used to compute the Euclidean distance between the centroids of the hexagonsn.
The following code calculates the pairwise distances between the bus stations represented by bs_num_sp. The spDists function from the sp package is employed for this purpose. The distances are computed based on the spatial coordinates of the bus stations, and the result is stored in the variable dist. The parameter longlat = FALSE indicates that the distances should be computed in the native coordinate system (not considering latitude and longitude as spherical coordinates).
dist <- spDists(bs_num_sp,
longlat = FALSE)head(dist, n=c(10, 10)) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8]
[1,] 0.000 750.000 3269.174 1500.000 2704.163 3968.627 1299.038 2250.000
[2,] 750.000 0.000 2598.076 750.000 1984.313 3269.174 750.000 1500.000
[3,] 3269.174 2598.076 0.000 1984.313 750.000 750.000 2704.163 1500.000
[4,] 1500.000 750.000 1984.313 0.000 1299.038 2598.076 750.000 750.000
[5,] 2704.163 1984.313 750.000 1299.038 0.000 1299.038 1984.313 750.000
[6,] 3968.627 3269.174 750.000 2598.076 1299.038 0.000 3269.174 1984.313
[7,] 1299.038 750.000 2704.163 750.000 1984.313 3269.174 0.000 1299.038
[8,] 2250.000 1500.000 1500.000 750.000 750.000 1984.313 1299.038 0.000
[9,] 3436.932 2704.163 750.000 1984.313 750.000 750.000 2598.076 1299.038
[10,] 4683.748 3968.627 1500.000 3269.174 1984.313 750.000 3897.114 2598.076
[,9] [,10]
[1,] 3436.932 4683.748
[2,] 2704.163 3968.627
[3,] 750.000 1500.000
[4,] 1984.313 3269.174
[5,] 750.000 1984.313
[6,] 750.000 750.000
[7,] 2598.076 3897.114
[8,] 1299.038 2598.076
[9,] 0.000 1299.038
[10,] 1299.038 0.0008.3 Labelling column and row heanders of a distance matrix
First, we will create a list sorted according to the the distance matrix by grid_id.
grid_id_names <- bs_num$grid_idNext we will attach grid_id to row and column for distance matrix matching ahead.
colnames(dist) <- paste0(grid_id_names)
rownames(dist) <- paste0(grid_id_names)8.3 Pivoting distance value by Hexagon grid
We will pivot the distance matrix into a long table by using the row and column grid_id as show in the code chunk below.
The melt operation reshapes the matrix into a long format.
distPair <- reshape2::melt(dist) %>%
rename(dist = value)
head(distPair, 10) Var1 Var2 dist
1 23 23 0.000
2 44 23 750.000
3 46 23 3269.174
4 66 23 1500.000
5 67 23 2704.163
6 68 23 3968.627
7 86 23 1299.038
8 87 23 2250.000
9 88 23 3436.932
10 89 23 4683.7488.4 Updating intra-zonal distances
First, we will select and find out the minimum value of the distance by using summary().
distPair %>%
filter(dist > 0) %>%
summary() Var1 Var2 dist
Min. : 23 Min. : 23 Min. : 750
1st Qu.: 871 1st Qu.: 871 1st Qu.: 8352
Median :1324 Median :1324 Median :13332
Mean :1269 Mean :1269 Mean :14162
3rd Qu.:1688 3rd Qu.:1688 3rd Qu.:18929
Max. :2505 Max. :2505 Max. :44680 The minimum distance is about 750, indicating travelling to adjacent hexagon.
Next, a constant distance value of 300 (middle to edge is 325) added into intra-zones distance.
distPair$dist <- ifelse(distPair$dist == 0,
300, distPair$dist)The code chunk below will be used to check the result data.frame.
distPair %>%
summary() Var1 Var2 dist
Min. : 23 Min. : 23 Min. : 300
1st Qu.: 871 1st Qu.: 871 1st Qu.: 8250
Median :1324 Median :1324 Median :13332
Mean :1269 Mean :1269 Mean :14145
3rd Qu.:1688 3rd Qu.:1688 3rd Qu.:18929
Max. :2505 Max. :2505 Max. :44680 The code chunk below is used to rename the origin and destination fields.
distPair <- distPair %>%
rename(ORIGIN_GRID_ID = Var1,
DESTIN_GRID_ID = Var2)
distPair %>% head() ORIGIN_GRID_ID DESTIN_GRID_ID dist
1 23 23 300.000
2 44 23 750.000
3 46 23 3269.174
4 66 23 1500.000
5 67 23 2704.163
6 68 23 3968.627glimpse(distPair)Rows: 695,556
Columns: 3
$ ORIGIN_GRID_ID <int> 23, 44, 46, 66, 67, 68, 86, 87, 88, 89, 90, 109, 110, 1…
$ DESTIN_GRID_ID <int> 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23,…
$ dist <dbl> 300.000, 750.000, 3269.174, 1500.000, 2704.163, 3968.62…9 Spatial Interaction Modelling
9.1 Preparing Flow Data
In general, we will calibrate separate Spatial Interaction Models for inter- and intra-zonal flows. we will focus our attention on inter-zonal flow. Hence, we need to exclude the intra-zonal flow from flow_data.
First, two new columns called FlowNoIntra and offset will be created by using the code chunk below.
flow_data$FlowNoIntra <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0, flow_data$MORNING_PEAK)
flow_data$offset <- ifelse(
flow_data$ORIGIN_SZ == flow_data$DESTIN_SZ,
0.000001, 1)Now, we need to combine flow data with distance value:
flow_data$ORIGIN_SZ <- as.factor(flow_data$ORIGIN_SZ)
flow_data$DESTIN_SZ <- as.factor(flow_data$DESTIN_SZ)
distPair$ORIGIN_GRID_ID <- as.factor(distPair$ORIGIN_GRID_ID)
distPair$DESTIN_GRID_ID <- as.factor(distPair$DESTIN_GRID_ID)flow_data1 <- flow_data %>%
left_join (distPair,
by = c("ORIGIN_SZ" = "ORIGIN_GRID_ID",
"DESTIN_SZ" = "DESTIN_GRID_ID"))we need to remove duplicate:
duplicate <- flow_data1 %>%
group_by_all() %>%
filter(n()>1) %>%
ungroup()SIM_data <- unique(flow_data1)According to the syntax used to derive values in FlowNoIntra field, all intra-zonal flow will be given a value of 0 or else the original flow values will be inserted.
Next, inter-zonal flow will be selected from flow_data and save into a new output data.frame called inter_zonal_flow by using the code chunk below.
inter_zonal_flow <- SIM_data %>%
filter(FlowNoIntra > 0)summary(inter_zonal_flow) ORIGIN_SZ DESTIN_SZ MORNING_PEAK BUSINESS_num
1960 : 298 1474 : 347 Min. : 1.0 Min. : 0.990
1474 : 292 1452 : 339 1st Qu.: 7.0 1st Qu.: 0.990
1477 : 292 1516 : 326 Median : 38.0 Median : 1.000
1496 : 278 1960 : 295 Mean : 385.1 Mean : 7.729
1623 : 277 1477 : 294 3rd Qu.: 180.0 3rd Qu.: 6.000
1749 : 273 1494 : 292 Max. :96644.0 Max. :97.000
(Other):63252 (Other):63069
FB_num lr_num schools_num hdb_num
Min. : 0.990 Min. : 0.990 Min. :0.990 Min. : 0.99
1st Qu.: 0.990 1st Qu.: 0.990 1st Qu.:0.990 1st Qu.: 0.99
Median : 0.990 Median : 1.000 Median :0.990 Median : 10.00
Mean : 6.306 Mean : 2.769 Mean :1.171 Mean : 19.76
3rd Qu.: 2.000 3rd Qu.: 3.000 3rd Qu.:1.000 3rd Qu.: 34.00
Max. :133.000 Max. :41.000 Max. :4.000 Max. :103.00
entertn_num FlowNoIntra offset dist
Min. :0.990 Min. : 1.0 Min. :1 Min. : 750
1st Qu.:0.990 1st Qu.: 7.0 1st Qu.:1 1st Qu.: 3000
Median :0.990 Median : 38.0 Median :1 Median : 5408
Mean :1.183 Mean : 385.1 Mean :1 Mean : 6334
3rd Qu.:0.990 3rd Qu.: 180.0 3rd Qu.:1 3rd Qu.: 8842
Max. :9.000 Max. :96644.0 Max. :1 Max. :24784
9.2 Visualising the dependent variable
Code
ggplot(data = inter_zonal_flow,
aes(x = MORNING_PEAK)) +
geom_histogram(fill="darkgreen")+
theme_minimal()
We can see that all ‘MORNING_PEAK’ values are all positive values and its distribution is highly skewed to the right side.
Next, let us visualise the relation between the dependent variable and one of the key independent variable in Spatial Interaction Model, namely distance.
Code
ggplot(data = inter_zonal_flow,
aes(x = dist,
y = MORNING_PEAK)) +
geom_point(color = "darkgreen") +
geom_smooth(method = lm, color = "yellow") +
theme_minimal()
Their relationship hardly resemble linear relationship.
When we plot the scatter plot by using the log transformed version of both variables, we can see that their relationship is more resemble linear relationship.
Code
ggplot(data = inter_zonal_flow,
aes(x = log(dist),
y = log(MORNING_PEAK))) +
geom_point(color = "darkgreen") +
geom_smooth(method = lm, color = "yellow")+
theme_minimal()
9.3 Correlation Analysis
Before I proceed to do SIM, I will determine if there are any correlations between the variables. Conducting a correlation analysis is vital as it reveals linear relationships between variables, aiding in the identification of associations. This process helps avoid multicollinearity issues, optimizing regression models by selecting pertinent variables.
inter_zonal_flow$BUSINESS_num <- as.numeric(inter_zonal_flow$BUSINESS_num)
inter_zonal_flow$FB_num<- as.numeric(inter_zonal_flow$FB_num)
inter_zonal_flow$lr_num <- as.numeric(inter_zonal_flow$lr_num)
inter_zonal_flow$schools_num <- as.numeric(inter_zonal_flow$schools_num)
inter_zonal_flow$hdb_num <- as.numeric(inter_zonal_flow$hdb_num)
inter_zonal_flow$entertn_num <- as.numeric(inter_zonal_flow$entertn_num)
inter_zonal_flow$MORNING_PEAK<- as.numeric(inter_zonal_flow$MORNING_PEAK)Now, we draw the correlation matrix:
Code
vars.cor <- cor(inter_zonal_flow[, 3:9])
corrplot(
vars.cor,
method = "ellipse",
lower = "ellipse",
upper = "number",
tl.pos = "lt",
diag = FALSE,
addCoef.col = "black",
tl.col = "black",
col = colorRampPalette(c("yellow", "white","lightgreen"))(100) ,number.cex = 0.7
)
The correlation analysis revealed a notable relationship between the variables “F&B” and “Leisure & Recreation” with a correlation coefficient exceeding 80%. This high correlation suggests a strong linear association between the two variables. As a result, it is advisable to retain only one of them in subsequent analyses to avoid issues of multicol-linearity.
Therefore, we choose to remove “Leisure & Recreation” and remain “F&B”. The following table is new explanatory variables to be used in the Spatial Interaction Modelling:
| No | Explanatory Variables |
|---|---|
| 1 | Business |
| 2 | F&B |
| 3 | schools |
| 4 | HDB |
| 5 | Entertainment |
9.4 Calibrating Spatial Interaction Models
9.4.1 Unconstrained Spatial Interaction Model
The code chunk used to calibrate to model is shown below:
uncSIM <- glm(formula = MORNING_PEAK ~
log(BUSINESS_num) +
log(FB_num) +
log(schools_num) +
log(hdb_num) +
log(entertn_num)+
log(dist),
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)the calculated R-squared is 0.12527437, indicating that the model accounts for approximately 12.53% of the variability in the observed MORNING_PEAK.
Code
CalcRSquared <- function(observed,estimated){
r <- cor(observed,estimated)
R2 <- r^2
R2
}
CalcRSquared(uncSIM$data$MORNING_PEAK, uncSIM$fitted.values)[1] 0.1247437Code
uncSIM$coefficients (Intercept) log(BUSINESS_num) log(FB_num) log(schools_num)
16.67686922 0.05927062 0.03310465 0.21753349
log(hdb_num) log(entertn_num) log(dist)
0.20942559 0.22414936 -1.41229192 Code
summary(uncSIM)
Call:
glm(formula = MORNING_PEAK ~ log(BUSINESS_num) + log(FB_num) +
log(schools_num) + log(hdb_num) + log(entertn_num) + log(dist),
family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 16.6768692 0.0019208 8682.0 <2e-16 ***
log(BUSINESS_num) 0.0592706 0.0001788 331.4 <2e-16 ***
log(FB_num) 0.0331046 0.0002402 137.8 <2e-16 ***
log(schools_num) 0.2175335 0.0006458 336.9 <2e-16 ***
log(hdb_num) 0.2094256 0.0001380 1517.7 <2e-16 ***
log(entertn_num) 0.2241494 0.0007501 298.8 <2e-16 ***
log(dist) -1.4122919 0.0002495 -5661.3 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 101244825 on 64961 degrees of freedom
Residual deviance: 62792208 on 64955 degrees of freedom
AIC: 63150592
Number of Fisher Scoring iterations: 79.4.2 Origin Constrained Model
Code chunk below shows the calibration of the model by using glm() of R and flow_data.
orcSIM <- glm(formula = MORNING_PEAK ~
ORIGIN_SZ +
log(BUSINESS_num) +
log(FB_num) +
log(schools_num) +
log(hdb_num) +
log(entertn_num)+
log(dist) - 1,
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)the calculated R-squared is 0.2402228, indicating that the model accounts for approximately 24.02% of the variability in the observed MORNING_PEAK.
Code
CalcRSquared(orcSIM$data$MORNING_PEAK, orcSIM$fitted.values)[1] 0.2402228Code
orcSIM$coefficients[818:823]log(BUSINESS_num) log(FB_num) log(schools_num) log(hdb_num)
0.1145699 0.1319546 0.1776087 0.1227611
log(entertn_num) log(dist)
0.2532727 -1.4416487 Code
summary(orcSIM)
Call:
glm(formula = MORNING_PEAK ~ ORIGIN_SZ + log(BUSINESS_num) +
log(FB_num) + log(schools_num) + log(hdb_num) + log(entertn_num) +
log(dist) - 1, family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
ORIGIN_SZ23 13.6371930 0.1270169 107.365 <2e-16 ***
ORIGIN_SZ44 14.3998717 0.1414392 101.810 <2e-16 ***
ORIGIN_SZ46 12.7403468 0.0924677 137.782 <2e-16 ***
ORIGIN_SZ66 13.5383719 0.1302054 103.977 <2e-16 ***
ORIGIN_SZ67 14.7573273 0.0259747 568.142 <2e-16 ***
ORIGIN_SZ68 12.8086473 0.1104479 115.970 <2e-16 ***
ORIGIN_SZ86 13.6730129 0.0803349 170.200 <2e-16 ***
ORIGIN_SZ87 15.3667022 0.0739574 207.778 <2e-16 ***
ORIGIN_SZ88 15.5861467 0.0189635 821.902 <2e-16 ***
ORIGIN_SZ89 13.5665982 0.0496043 273.497 <2e-16 ***
ORIGIN_SZ90 12.9063595 0.1231060 104.839 <2e-16 ***
ORIGIN_SZ109 13.5231995 0.0894638 151.158 <2e-16 ***
ORIGIN_SZ110 13.7067486 0.0762736 179.705 <2e-16 ***
ORIGIN_SZ111 16.5576703 0.0114502 1446.065 <2e-16 ***
ORIGIN_SZ112 12.8861335 0.0685468 187.990 <2e-16 ***
ORIGIN_SZ128 16.1234129 0.0232791 692.612 <2e-16 ***
ORIGIN_SZ129 13.1831647 0.1767892 74.570 <2e-16 ***
ORIGIN_SZ130 14.1769985 0.0527377 268.821 <2e-16 ***
ORIGIN_SZ131 14.4127053 0.0316185 455.831 <2e-16 ***
ORIGIN_SZ132 13.2849004 0.0532608 249.431 <2e-16 ***
ORIGIN_SZ133 13.5237671 0.0408696 330.900 <2e-16 ***
ORIGIN_SZ134 15.8966693 0.0242145 656.493 <2e-16 ***
ORIGIN_SZ150 16.2978631 0.0198543 820.871 <2e-16 ***
ORIGIN_SZ151 13.3718598 0.0662482 201.845 <2e-16 ***
ORIGIN_SZ152 12.6979398 0.0824984 153.917 <2e-16 ***
ORIGIN_SZ153 14.0984175 0.0420025 335.656 <2e-16 ***
ORIGIN_SZ154 16.6825926 0.0090750 1838.297 <2e-16 ***
ORIGIN_SZ155 13.5966151 0.0355186 382.802 <2e-16 ***
ORIGIN_SZ156 14.4620608 0.0435180 332.324 <2e-16 ***
ORIGIN_SZ172 14.9911064 0.0639192 234.532 <2e-16 ***
ORIGIN_SZ174 13.9885171 0.0470199 297.502 <2e-16 ***
ORIGIN_SZ175 16.0977944 0.0103197 1559.915 <2e-16 ***
ORIGIN_SZ176 17.2536974 0.0062502 2760.506 <2e-16 ***
ORIGIN_SZ195 13.0764242 0.0781080 167.415 <2e-16 ***
ORIGIN_SZ196 13.6161083 0.0386532 352.263 <2e-16 ***
ORIGIN_SZ197 12.5024177 0.1240488 100.786 <2e-16 ***
ORIGIN_SZ215 13.9064176 0.0864108 160.934 <2e-16 ***
ORIGIN_SZ216 17.5183224 0.0053407 3280.184 <2e-16 ***
ORIGIN_SZ217 14.8690446 0.0212652 699.221 <2e-16 ***
ORIGIN_SZ237 12.5225365 0.1666773 75.130 <2e-16 ***
ORIGIN_SZ238 13.2478875 0.0712749 185.870 <2e-16 ***
ORIGIN_SZ239 13.5878274 0.1360979 99.839 <2e-16 ***
ORIGIN_SZ257 13.5014239 0.0577665 233.724 <2e-16 ***
ORIGIN_SZ258 14.4462515 0.0285670 505.696 <2e-16 ***
ORIGIN_SZ259 14.2502358 0.0396690 359.228 <2e-16 ***
ORIGIN_SZ278 15.2806884 0.0346581 440.899 <2e-16 ***
ORIGIN_SZ279 13.2379013 0.0441496 299.842 <2e-16 ***
ORIGIN_SZ280 13.6300652 0.0479320 284.363 <2e-16 ***
ORIGIN_SZ298 10.8564638 0.3333387 32.569 <2e-16 ***
ORIGIN_SZ299 13.3702118 0.0523537 255.382 <2e-16 ***
ORIGIN_SZ300 16.5175377 0.0085691 1927.569 <2e-16 ***
ORIGIN_SZ320 13.8490521 0.0489461 282.945 <2e-16 ***
ORIGIN_SZ321 13.8203889 0.0747682 184.843 <2e-16 ***
ORIGIN_SZ322 14.7251265 0.0400786 367.406 <2e-16 ***
ORIGIN_SZ340 15.1031677 0.0271520 556.245 <2e-16 ***
ORIGIN_SZ341 13.6159022 0.0449413 302.971 <2e-16 ***
ORIGIN_SZ342 14.3919596 0.0401117 358.797 <2e-16 ***
ORIGIN_SZ363 15.1936277 0.0371860 408.585 <2e-16 ***
ORIGIN_SZ364 14.9481077 0.0265721 562.548 <2e-16 ***
ORIGIN_SZ383 14.4593095 0.0306462 471.813 <2e-16 ***
ORIGIN_SZ384 13.3345107 0.0488324 273.067 <2e-16 ***
ORIGIN_SZ385 14.6340720 0.0465590 314.313 <2e-16 ***
ORIGIN_SZ404 15.3464320 0.0290339 528.569 <2e-16 ***
ORIGIN_SZ405 14.1098214 0.0514680 274.148 <2e-16 ***
ORIGIN_SZ406 18.4385147 0.0030793 5987.858 <2e-16 ***
ORIGIN_SZ407 14.9931251 0.0390034 384.405 <2e-16 ***
ORIGIN_SZ408 15.6956577 0.0197654 794.099 <2e-16 ***
ORIGIN_SZ425 12.6447000 0.0966917 130.773 <2e-16 ***
ORIGIN_SZ426 14.4895031 0.0302644 478.763 <2e-16 ***
ORIGIN_SZ427 13.3984445 0.0423405 316.445 <2e-16 ***
ORIGIN_SZ428 13.6274613 0.0739488 184.282 <2e-16 ***
ORIGIN_SZ429 16.1986156 0.0173204 935.232 <2e-16 ***
ORIGIN_SZ446 14.1674529 0.0583537 242.786 <2e-16 ***
ORIGIN_SZ447 13.7207898 0.0402379 340.991 <2e-16 ***
ORIGIN_SZ448 14.5657430 0.0270316 538.842 <2e-16 ***
ORIGIN_SZ449 17.3659003 0.0062471 2779.836 <2e-16 ***
ORIGIN_SZ450 15.5758092 0.0174042 894.948 <2e-16 ***
ORIGIN_SZ468 14.6220318 0.0306029 477.798 <2e-16 ***
ORIGIN_SZ469 15.4969625 0.0151304 1024.228 <2e-16 ***
ORIGIN_SZ470 17.8317688 0.0046273 3853.623 <2e-16 ***
ORIGIN_SZ471 16.3895329 0.0146396 1119.533 <2e-16 ***
ORIGIN_SZ488 14.2719675 0.0553340 257.924 <2e-16 ***
ORIGIN_SZ489 11.7898296 0.1601388 73.623 <2e-16 ***
ORIGIN_SZ490 16.0200378 0.0123690 1295.177 <2e-16 ***
ORIGIN_SZ491 16.5599799 0.0077078 2148.476 <2e-16 ***
ORIGIN_SZ493 11.6084215 0.1690415 68.672 <2e-16 ***
ORIGIN_SZ494 13.6638105 0.0626515 218.092 <2e-16 ***
ORIGIN_SZ509 14.2544412 0.0365823 389.654 <2e-16 ***
ORIGIN_SZ510 14.8590608 0.0252682 588.055 <2e-16 ***
ORIGIN_SZ511 15.6890545 0.0110488 1419.978 <2e-16 ***
ORIGIN_SZ512 18.2483529 0.0034565 5279.402 <2e-16 ***
ORIGIN_SZ513 14.9710746 0.0244058 613.422 <2e-16 ***
ORIGIN_SZ514 14.2955817 0.0388243 368.213 <2e-16 ***
ORIGIN_SZ515 12.0129762 0.1525101 78.768 <2e-16 ***
ORIGIN_SZ530 13.5662242 0.0870589 155.828 <2e-16 ***
ORIGIN_SZ531 14.8866777 0.0193348 769.944 <2e-16 ***
ORIGIN_SZ532 14.1788122 0.0252809 560.851 <2e-16 ***
ORIGIN_SZ533 18.1101815 0.0034565 5239.399 <2e-16 ***
ORIGIN_SZ534 18.3426395 0.0037958 4832.369 <2e-16 ***
ORIGIN_SZ536 14.9570996 0.0252874 591.485 <2e-16 ***
ORIGIN_SZ537 12.6594397 0.1221845 103.609 <2e-16 ***
ORIGIN_SZ538 12.9636969 0.2085257 62.168 <2e-16 ***
ORIGIN_SZ539 11.7682512 1.0000024 11.768 <2e-16 ***
ORIGIN_SZ551 13.6201379 0.0530872 256.561 <2e-16 ***
ORIGIN_SZ552 15.6980843 0.0361772 433.921 <2e-16 ***
ORIGIN_SZ553 14.7751096 0.0174875 844.894 <2e-16 ***
ORIGIN_SZ554 18.0270233 0.0037604 4793.855 <2e-16 ***
ORIGIN_SZ555 17.4175108 0.0069378 2510.514 <2e-16 ***
ORIGIN_SZ559 13.4044730 0.0976085 137.329 <2e-16 ***
ORIGIN_SZ560 15.5654515 0.0450009 345.892 <2e-16 ***
ORIGIN_SZ561 9.4248423 1.0000015 9.425 <2e-16 ***
ORIGIN_SZ572 10.6932892 0.4082524 26.193 <2e-16 ***
ORIGIN_SZ573 13.8999804 0.0419978 330.969 <2e-16 ***
ORIGIN_SZ574 14.8602990 0.0368346 403.433 <2e-16 ***
ORIGIN_SZ575 18.8258723 0.0025888 7272.166 <2e-16 ***
ORIGIN_SZ576 17.4929353 0.0049323 3546.622 <2e-16 ***
ORIGIN_SZ578 12.7145754 0.0976084 130.261 <2e-16 ***
ORIGIN_SZ582 13.0664380 0.1048447 124.627 <2e-16 ***
ORIGIN_SZ583 12.8770345 0.4082548 31.542 <2e-16 ***
ORIGIN_SZ584 15.6344658 0.0514784 303.709 <2e-16 ***
ORIGIN_SZ593 14.0990971 0.0482095 292.455 <2e-16 ***
ORIGIN_SZ594 15.0264706 0.0252806 594.387 <2e-16 ***
ORIGIN_SZ595 14.5664960 0.0188263 773.731 <2e-16 ***
ORIGIN_SZ596 17.3914121 0.0043625 3986.534 <2e-16 ***
ORIGIN_SZ597 13.9937538 0.0573885 243.842 <2e-16 ***
ORIGIN_SZ603 13.2842312 0.1097807 121.007 <2e-16 ***
ORIGIN_SZ604 13.9890671 0.1825893 76.615 <2e-16 ***
ORIGIN_SZ615 13.2733065 0.0459705 288.735 <2e-16 ***
ORIGIN_SZ616 14.1815503 0.0313998 451.644 <2e-16 ***
ORIGIN_SZ617 15.0887684 0.0181672 830.548 <2e-16 ***
ORIGIN_SZ618 17.8726200 0.0038927 4591.345 <2e-16 ***
ORIGIN_SZ620 14.6951703 0.0298798 491.810 <2e-16 ***
ORIGIN_SZ637 13.7311618 0.0414944 330.916 <2e-16 ***
ORIGIN_SZ638 17.4594446 0.0042411 4116.696 <2e-16 ***
ORIGIN_SZ657 15.3266460 0.0164622 931.018 <2e-16 ***
ORIGIN_SZ658 16.6465542 0.0063674 2614.324 <2e-16 ***
ORIGIN_SZ659 17.0727059 0.0054192 3150.409 <2e-16 ***
ORIGIN_SZ660 18.0546541 0.0034751 5195.497 <2e-16 ***
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ORIGIN_SZ1938 17.3455486 0.0043828 3957.627 <2e-16 ***
ORIGIN_SZ1939 18.0078675 0.0040139 4486.418 <2e-16 ***
ORIGIN_SZ1942 14.0925286 0.0403380 349.361 <2e-16 ***
ORIGIN_SZ1959 16.2200261 0.0082820 1958.465 <2e-16 ***
ORIGIN_SZ1960 18.0723157 0.0030375 5949.683 <2e-16 ***
ORIGIN_SZ1961 16.8535335 0.0067221 2507.201 <2e-16 ***
ORIGIN_SZ1962 17.7409672 0.0043092 4116.982 <2e-16 ***
ORIGIN_SZ1964 13.2553789 0.0824997 160.672 <2e-16 ***
ORIGIN_SZ1979 16.4881568 0.0076982 2141.828 <2e-16 ***
ORIGIN_SZ1980 14.9708840 0.0136317 1098.240 <2e-16 ***
ORIGIN_SZ1981 17.4290066 0.0042820 4070.277 <2e-16 ***
ORIGIN_SZ1982 16.1847782 0.0106877 1514.338 <2e-16 ***
ORIGIN_SZ1983 17.7131611 0.0043282 4092.456 <2e-16 ***
ORIGIN_SZ1984 16.3401353 0.0074844 2183.220 <2e-16 ***
ORIGIN_SZ1985 16.9405376 0.0061212 2767.505 <2e-16 ***
ORIGIN_SZ2001 16.7667188 0.0057133 2934.668 <2e-16 ***
ORIGIN_SZ2002 17.4727864 0.0038369 4553.877 <2e-16 ***
ORIGIN_SZ2003 17.0717267 0.0049328 3460.869 <2e-16 ***
ORIGIN_SZ2004 17.8259362 0.0041105 4336.711 <2e-16 ***
ORIGIN_SZ2005 17.5889461 0.0041274 4261.480 <2e-16 ***
ORIGIN_SZ2006 16.1202663 0.0090163 1787.904 <2e-16 ***
ORIGIN_SZ2007 15.4587971 0.0158466 975.526 <2e-16 ***
ORIGIN_SZ2022 17.4262785 0.0056351 3092.458 <2e-16 ***
ORIGIN_SZ2023 17.6779653 0.0037277 4742.336 <2e-16 ***
ORIGIN_SZ2024 17.0342910 0.0047127 3614.563 <2e-16 ***
ORIGIN_SZ2025 17.2883254 0.0045580 3792.953 <2e-16 ***
ORIGIN_SZ2026 15.7631450 0.0112095 1406.230 <2e-16 ***
ORIGIN_SZ2027 17.7824851 0.0039759 4472.618 <2e-16 ***
ORIGIN_SZ2043 16.5064888 0.0074455 2216.968 <2e-16 ***
ORIGIN_SZ2044 17.4164845 0.0042103 4136.644 <2e-16 ***
ORIGIN_SZ2045 13.5484660 0.0644455 210.231 <2e-16 ***
ORIGIN_SZ2046 17.4220788 0.0039175 4447.205 <2e-16 ***
ORIGIN_SZ2047 17.3312549 0.0051236 3382.660 <2e-16 ***
ORIGIN_SZ2048 17.4222120 0.0045355 3841.271 <2e-16 ***
ORIGIN_SZ2049 16.2697515 0.0128016 1270.915 <2e-16 ***
ORIGIN_SZ2064 17.3422374 0.0047956 3616.317 <2e-16 ***
ORIGIN_SZ2065 15.9824887 0.0081983 1949.491 <2e-16 ***
ORIGIN_SZ2066 15.8922658 0.0228202 696.414 <2e-16 ***
ORIGIN_SZ2067 18.3077411 0.0028639 6392.632 <2e-16 ***
ORIGIN_SZ2068 17.5972042 0.0066806 2634.056 <2e-16 ***
ORIGIN_SZ2069 17.2219369 0.0053081 3244.459 <2e-16 ***
ORIGIN_SZ2085 16.0881664 0.0091778 1752.950 <2e-16 ***
ORIGIN_SZ2086 17.6215580 0.0039714 4437.060 <2e-16 ***
ORIGIN_SZ2087 16.3950722 0.0068826 2382.112 <2e-16 ***
ORIGIN_SZ2088 17.0908524 0.0045294 3773.308 <2e-16 ***
ORIGIN_SZ2089 16.8675590 0.0062539 2697.132 <2e-16 ***
ORIGIN_SZ2090 17.8315057 0.0034963 5100.146 <2e-16 ***
ORIGIN_SZ2091 13.6955859 0.0631468 216.885 <2e-16 ***
ORIGIN_SZ2105 14.1125812 0.0985581 143.190 <2e-16 ***
ORIGIN_SZ2106 14.6414654 0.0184780 792.373 <2e-16 ***
ORIGIN_SZ2107 15.8314290 0.0086402 1832.308 <2e-16 ***
ORIGIN_SZ2108 17.0084994 0.0053738 3165.070 <2e-16 ***
ORIGIN_SZ2109 17.2431047 0.0044610 3865.294 <2e-16 ***
ORIGIN_SZ2110 16.7916912 0.0071236 2357.179 <2e-16 ***
ORIGIN_SZ2111 14.6874255 0.0384227 382.259 <2e-16 ***
ORIGIN_SZ2128 15.6840940 0.0134195 1168.751 <2e-16 ***
ORIGIN_SZ2129 15.0891198 0.0146034 1033.258 <2e-16 ***
ORIGIN_SZ2130 17.4880134 0.0038775 4510.177 <2e-16 ***
ORIGIN_SZ2131 17.7697711 0.0043766 4060.181 <2e-16 ***
ORIGIN_SZ2132 16.9092159 0.0058602 2885.430 <2e-16 ***
ORIGIN_SZ2148 16.3905292 0.0109595 1495.556 <2e-16 ***
ORIGIN_SZ2149 15.2995992 0.0145826 1049.169 <2e-16 ***
ORIGIN_SZ2150 17.5091513 0.0044395 3943.917 <2e-16 ***
ORIGIN_SZ2151 17.7314741 0.0035096 5052.291 <2e-16 ***
ORIGIN_SZ2152 17.9129001 0.0037585 4765.994 <2e-16 ***
ORIGIN_SZ2153 17.3432375 0.0053764 3225.829 <2e-16 ***
ORIGIN_SZ2171 16.4568918 0.0068831 2390.905 <2e-16 ***
ORIGIN_SZ2172 16.6154908 0.0075332 2205.632 <2e-16 ***
ORIGIN_SZ2173 16.9974571 0.0050314 3378.252 <2e-16 ***
ORIGIN_SZ2174 17.2830673 0.0051222 3374.153 <2e-16 ***
ORIGIN_SZ2191 16.2413756 0.0097908 1658.837 <2e-16 ***
ORIGIN_SZ2192 15.8054056 0.0106206 1488.190 <2e-16 ***
ORIGIN_SZ2193 16.8469406 0.0058486 2880.520 <2e-16 ***
ORIGIN_SZ2194 17.0847071 0.0050136 3407.670 <2e-16 ***
ORIGIN_SZ2195 16.5157113 0.0199754 826.803 <2e-16 ***
ORIGIN_SZ2212 14.0634543 0.0825044 170.457 <2e-16 ***
ORIGIN_SZ2213 14.0099431 0.0361596 387.447 <2e-16 ***
ORIGIN_SZ2214 14.8668683 0.0261041 569.523 <2e-16 ***
ORIGIN_SZ2215 16.7813055 0.0064734 2592.339 <2e-16 ***
ORIGIN_SZ2216 15.8040514 0.0106287 1486.925 <2e-16 ***
ORIGIN_SZ2233 14.1499603 0.0438945 322.363 <2e-16 ***
ORIGIN_SZ2234 16.3120143 0.0191588 851.412 <2e-16 ***
ORIGIN_SZ2235 15.8017816 0.0123113 1283.516 <2e-16 ***
ORIGIN_SZ2236 15.6094875 0.0125479 1243.990 <2e-16 ***
ORIGIN_SZ2237 13.3065457 0.0559328 237.902 <2e-16 ***
ORIGIN_SZ2256 14.2009275 0.0418181 339.588 <2e-16 ***
ORIGIN_SZ2257 15.2607057 0.0188763 808.459 <2e-16 ***
ORIGIN_SZ2258 14.8781858 0.0154325 964.084 <2e-16 ***
ORIGIN_SZ2259 14.5573336 0.0330605 440.324 <2e-16 ***
ORIGIN_SZ2277 15.2450083 0.0366627 415.818 <2e-16 ***
ORIGIN_SZ2278 16.2711543 0.0113003 1439.893 <2e-16 ***
ORIGIN_SZ2279 14.6778939 0.0195616 750.342 <2e-16 ***
ORIGIN_SZ2280 12.6841698 0.1031584 122.958 <2e-16 ***
ORIGIN_SZ2297 17.2675039 0.0088944 1941.382 <2e-16 ***
ORIGIN_SZ2300 13.1130468 0.0674481 194.417 <2e-16 ***
ORIGIN_SZ2301 14.8744683 0.0182382 815.568 <2e-16 ***
ORIGIN_SZ2318 15.6275373 0.0179566 870.293 <2e-16 ***
ORIGIN_SZ2319 16.6558082 0.0099014 1682.170 <2e-16 ***
ORIGIN_SZ2322 16.1067660 0.0112754 1428.491 <2e-16 ***
ORIGIN_SZ2337 17.2852700 0.0146577 1179.264 <2e-16 ***
ORIGIN_SZ2341 16.9876357 0.0088480 1919.947 <2e-16 ***
ORIGIN_SZ2343 15.6464859 0.0135032 1158.721 <2e-16 ***
ORIGIN_SZ2361 16.6635165 0.0112716 1478.363 <2e-16 ***
ORIGIN_SZ2364 12.9334479 0.0733497 176.326 <2e-16 ***
ORIGIN_SZ2379 17.1237880 0.0162800 1051.832 <2e-16 ***
ORIGIN_SZ2384 16.2321989 0.0143144 1133.975 <2e-16 ***
ORIGIN_SZ2405 15.9593360 0.0143219 1114.335 <2e-16 ***
ORIGIN_SZ2406 14.5887345 0.0323372 451.144 <2e-16 ***
ORIGIN_SZ2426 16.3970030 0.0256370 639.583 <2e-16 ***
ORIGIN_SZ2427 16.9094915 0.0104303 1621.196 <2e-16 ***
ORIGIN_SZ2505 16.6423985 0.0384692 432.616 <2e-16 ***
log(BUSINESS_num) 0.1145699 0.0001897 604.087 <2e-16 ***
log(FB_num) 0.1319546 0.0002589 509.608 <2e-16 ***
log(schools_num) 0.1776087 0.0006586 269.689 <2e-16 ***
log(hdb_num) 0.1227611 0.0001474 832.701 <2e-16 ***
log(entertn_num) 0.2532727 0.0007717 328.190 <2e-16 ***
log(dist) -1.4416487 0.0002609 -5526.339 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 349181331 on 64962 degrees of freedom
Residual deviance: 42866101 on 64139 degrees of freedom
AIC: 43226117
Number of Fisher Scoring iterations: 79.4.3 Destin Constrained Model
The code chunk used to calibrate to model is shown below is the destination:
decSIM <- glm(formula = MORNING_PEAK ~
DESTIN_SZ +
log(BUSINESS_num) +
log(FB_num) +
log(schools_num) +
log(hdb_num) +
log(entertn_num)+
log(dist)-1,
family = poisson(link = "log"),
data = inter_zonal_flow,
na.action = na.exclude)the calculated R-squared is 0.3053515, indicating that the model accounts for approximately 30.54% of the variability in the observed MORNING_PEAK.
Code
CalcRSquared(decSIM$data$MORNING_PEAK, decSIM$fitted.values)[1] 0.3053515Code
decSIM$coefficients[820:825]log(BUSINESS_num) log(FB_num) log(schools_num) log(hdb_num)
NA NA NA NA
log(entertn_num) log(dist)
NA -1.461883 Code
options(max.print = 10000)
summary(decSIM)
Call:
glm(formula = MORNING_PEAK ~ DESTIN_SZ + log(BUSINESS_num) +
log(FB_num) + log(schools_num) + log(hdb_num) + log(entertn_num) +
log(dist) - 1, family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients: (5 not defined because of singularities)
Estimate Std. Error z value Pr(>|z|)
DESTIN_SZ23 16.6350037 0.0504877 329.49 <2e-16 ***
DESTIN_SZ44 17.7648906 0.0226652 783.79 <2e-16 ***
DESTIN_SZ46 16.8708169 0.0191462 881.16 <2e-16 ***
DESTIN_SZ66 15.9389708 0.0461679 345.24 <2e-16 ***
DESTIN_SZ67 16.7983647 0.0137218 1224.21 <2e-16 ***
DESTIN_SZ68 16.8163886 0.0193076 870.97 <2e-16 ***
DESTIN_SZ86 16.8940255 0.0344631 490.21 <2e-16 ***
DESTIN_SZ87 13.9580875 0.0836436 166.88 <2e-16 ***
DESTIN_SZ88 16.2107274 0.0171040 947.77 <2e-16 ***
DESTIN_SZ89 16.6972232 0.0199974 834.97 <2e-16 ***
DESTIN_SZ90 12.1872374 0.7071097 17.23 <2e-16 ***
DESTIN_SZ109 15.9090781 0.0240970 660.21 <2e-16 ***
DESTIN_SZ110 13.0822409 0.1005198 130.15 <2e-16 ***
DESTIN_SZ111 16.7511015 0.0118668 1411.60 <2e-16 ***
DESTIN_SZ112 14.9617633 0.0323917 461.90 <2e-16 ***
DESTIN_SZ128 16.6176074 0.0231683 717.25 <2e-16 ***
DESTIN_SZ129 13.5696912 0.1324650 102.44 <2e-16 ***
DESTIN_SZ130 15.9680273 0.0219343 728.00 <2e-16 ***
DESTIN_SZ131 15.4024371 0.0217725 707.43 <2e-16 ***
DESTIN_SZ132 16.6387249 0.0146895 1132.69 <2e-16 ***
DESTIN_SZ133 16.4221307 0.0123079 1334.28 <2e-16 ***
DESTIN_SZ134 16.6149515 0.0115366 1440.19 <2e-16 ***
DESTIN_SZ150 16.0520048 0.0253139 634.12 <2e-16 ***
DESTIN_SZ151 15.7327201 0.0222516 707.04 <2e-16 ***
DESTIN_SZ152 17.1756622 0.0142121 1208.53 <2e-16 ***
DESTIN_SZ153 16.9664862 0.0129691 1308.23 <2e-16 ***
DESTIN_SZ154 15.1305365 0.0271986 556.30 <2e-16 ***
DESTIN_SZ155 15.8372324 0.0184088 860.31 <2e-16 ***
DESTIN_SZ156 16.3358762 0.0196674 830.61 <2e-16 ***
DESTIN_SZ172 14.5845392 0.0430694 338.63 <2e-16 ***
DESTIN_SZ174 16.4021989 0.0143354 1144.18 <2e-16 ***
DESTIN_SZ175 16.5471268 0.0104815 1578.70 <2e-16 ***
DESTIN_SZ176 14.9585939 0.0264885 564.72 <2e-16 ***
DESTIN_SZ195 15.7298146 0.0295692 531.97 <2e-16 ***
DESTIN_SZ196 16.6844551 0.0100408 1661.67 <2e-16 ***
DESTIN_SZ197 13.4886576 0.0751863 179.40 <2e-16 ***
DESTIN_SZ215 16.5514188 0.0290274 570.20 <2e-16 ***
DESTIN_SZ216 15.8626889 0.0152046 1043.28 <2e-16 ***
DESTIN_SZ217 17.2783169 0.0091383 1890.76 <2e-16 ***
DESTIN_SZ237 16.1171510 0.0305242 528.01 <2e-16 ***
DESTIN_SZ238 16.6697988 0.0147529 1129.93 <2e-16 ***
DESTIN_SZ239 15.6539571 0.0301673 518.90 <2e-16 ***
DESTIN_SZ257 16.4832448 0.0154009 1070.28 <2e-16 ***
DESTIN_SZ258 15.9682169 0.0190669 837.48 <2e-16 ***
DESTIN_SZ259 17.1908916 0.0118314 1452.99 <2e-16 ***
DESTIN_SZ278 16.7794448 0.0137832 1217.38 <2e-16 ***
DESTIN_SZ279 16.4807373 0.0130646 1261.48 <2e-16 ***
DESTIN_SZ280 16.8293849 0.0122569 1373.06 <2e-16 ***
DESTIN_SZ298 13.6812668 0.1291111 105.97 <2e-16 ***
DESTIN_SZ299 16.6761994 0.0157800 1056.80 <2e-16 ***
DESTIN_SZ300 15.8888699 0.0167336 949.52 <2e-16 ***
DESTIN_SZ320 17.1120970 0.0137400 1245.42 <2e-16 ***
DESTIN_SZ321 15.8931575 0.0233389 680.97 <2e-16 ***
DESTIN_SZ322 17.9990148 0.0114968 1565.56 <2e-16 ***
DESTIN_SZ340 18.0084556 0.0105046 1714.34 <2e-16 ***
DESTIN_SZ341 16.8407452 0.0119767 1406.13 <2e-16 ***
DESTIN_SZ342 17.8472835 0.0102467 1741.75 <2e-16 ***
DESTIN_SZ363 17.0920934 0.0130186 1312.90 <2e-16 ***
DESTIN_SZ364 18.1472210 0.0076257 2379.75 <2e-16 ***
DESTIN_SZ383 17.1539570 0.0087594 1958.34 <2e-16 ***
DESTIN_SZ384 18.2281528 0.0082303 2214.77 <2e-16 ***
DESTIN_SZ385 17.2050842 0.0145717 1180.72 <2e-16 ***
DESTIN_SZ404 17.8057962 0.0123818 1438.07 <2e-16 ***
DESTIN_SZ405 17.2056191 0.0102264 1682.48 <2e-16 ***
DESTIN_SZ406 17.5162432 0.0051447 3404.71 <2e-16 ***
DESTIN_SZ407 18.8769281 0.0076649 2462.76 <2e-16 ***
DESTIN_SZ408 19.3525187 0.0043373 4461.89 <2e-16 ***
DESTIN_SZ425 15.7913467 0.0243422 648.72 <2e-16 ***
DESTIN_SZ426 17.0046451 0.0100827 1686.52 <2e-16 ***
DESTIN_SZ427 15.0595385 0.0227629 661.58 <2e-16 ***
DESTIN_SZ428 17.4326472 0.0096489 1806.69 <2e-16 ***
DESTIN_SZ429 16.7217277 0.0212361 787.42 <2e-16 ***
DESTIN_SZ446 17.1256672 0.0223256 767.09 <2e-16 ***
DESTIN_SZ447 16.0327727 0.0168113 953.69 <2e-16 ***
DESTIN_SZ448 17.0192011 0.0114702 1483.78 <2e-16 ***
DESTIN_SZ449 17.7883748 0.0069594 2556.02 <2e-16 ***
DESTIN_SZ450 16.9471362 0.0110126 1538.89 <2e-16 ***
DESTIN_SZ468 17.2399857 0.0105525 1633.73 <2e-16 ***
DESTIN_SZ469 17.1924367 0.0083100 2068.88 <2e-16 ***
DESTIN_SZ470 17.5791594 0.0065198 2696.29 <2e-16 ***
DESTIN_SZ471 16.5772156 0.0152953 1083.81 <2e-16 ***
DESTIN_SZ488 16.1865316 0.0217661 743.66 <2e-16 ***
DESTIN_SZ489 14.7212952 0.0457261 321.94 <2e-16 ***
DESTIN_SZ490 17.3463466 0.0084917 2042.74 <2e-16 ***
DESTIN_SZ491 15.9770695 0.0148026 1079.34 <2e-16 ***
DESTIN_SZ493 14.3167122 0.0477080 300.09 <2e-16 ***
DESTIN_SZ494 16.2070130 0.0216343 749.14 <2e-16 ***
DESTIN_SZ509 15.9972914 0.0147449 1084.94 <2e-16 ***
DESTIN_SZ510 17.3356293 0.0096472 1796.97 <2e-16 ***
DESTIN_SZ511 17.2671211 0.0066432 2599.22 <2e-16 ***
DESTIN_SZ512 17.3427742 0.0063618 2726.09 <2e-16 ***
DESTIN_SZ513 17.7464204 0.0072148 2459.71 <2e-16 ***
DESTIN_SZ514 16.9224595 0.0116174 1456.64 <2e-16 ***
DESTIN_SZ515 15.6696805 0.0296989 527.62 <2e-16 ***
DESTIN_SZ530 15.3908524 0.0283953 542.02 <2e-16 ***
DESTIN_SZ531 17.9922198 0.0058826 3058.57 <2e-16 ***
DESTIN_SZ532 16.9617561 0.0087074 1947.97 <2e-16 ***
DESTIN_SZ533 18.9405165 0.0031746 5966.21 <2e-16 ***
DESTIN_SZ534 17.6841769 0.0063900 2767.49 <2e-16 ***
DESTIN_SZ536 15.8542723 0.0175085 905.52 <2e-16 ***
DESTIN_SZ537 15.3354540 0.0333316 460.09 <2e-16 ***
DESTIN_SZ538 15.0159050 0.0426815 351.81 <2e-16 ***
DESTIN_SZ539 14.0001197 0.2500093 56.00 <2e-16 ***
DESTIN_SZ551 16.3176984 0.0173472 940.65 <2e-16 ***
DESTIN_SZ552 18.6362388 0.0103292 1804.23 <2e-16 ***
DESTIN_SZ553 16.9884919 0.0084946 1999.93 <2e-16 ***
DESTIN_SZ554 17.3254481 0.0066826 2592.61 <2e-16 ***
DESTIN_SZ555 17.6793305 0.0073795 2395.72 <2e-16 ***
DESTIN_SZ559 15.6614521 0.0529668 295.68 <2e-16 ***
DESTIN_SZ560 16.9584128 0.0161495 1050.09 <2e-16 ***
DESTIN_SZ561 15.6756427 0.0641880 244.21 <2e-16 ***
DESTIN_SZ572 16.5303733 0.0342533 482.59 <2e-16 ***
DESTIN_SZ573 17.2474249 0.0099580 1732.02 <2e-16 ***
DESTIN_SZ574 17.1383588 0.0154267 1110.95 <2e-16 ***
DESTIN_SZ575 19.4038343 0.0025184 7704.92 <2e-16 ***
DESTIN_SZ576 17.4550171 0.0062076 2811.90 <2e-16 ***
DESTIN_SZ578 13.2867423 0.0976082 136.12 <2e-16 ***
DESTIN_SZ582 14.8272003 0.0612279 242.16 <2e-16 ***
DESTIN_SZ583 13.6634209 0.1825843 74.83 <2e-16 ***
DESTIN_SZ584 16.6164471 0.0343869 483.22 <2e-16 ***
DESTIN_SZ593 15.7980949 0.0249032 634.38 <2e-16 ***
DESTIN_SZ594 16.6145107 0.0133112 1248.16 <2e-16 ***
DESTIN_SZ595 17.6899936 0.0058536 3022.09 <2e-16 ***
DESTIN_SZ596 17.6715881 0.0050997 3465.24 <2e-16 ***
DESTIN_SZ597 17.3190976 0.0149428 1159.03 <2e-16 ***
DESTIN_SZ603 14.7314038 0.0511291 288.12 <2e-16 ***
DESTIN_SZ604 16.9938545 0.0492599 344.98 <2e-16 ***
DESTIN_SZ615 15.9197596 0.0144271 1103.46 <2e-16 ***
DESTIN_SZ616 17.4648127 0.0086819 2011.64 <2e-16 ***
DESTIN_SZ617 16.5733942 0.0090141 1838.61 <2e-16 ***
DESTIN_SZ618 17.4535085 0.0062524 2791.51 <2e-16 ***
DESTIN_SZ620 17.1285449 0.0106657 1605.95 <2e-16 ***
DESTIN_SZ637 16.9761427 0.0107006 1586.47 <2e-16 ***
DESTIN_SZ638 17.4409559 0.0057167 3050.87 <2e-16 ***
DESTIN_SZ657 17.5626225 0.0070019 2508.27 <2e-16 ***
DESTIN_SZ658 17.3208974 0.0060701 2853.49 <2e-16 ***
DESTIN_SZ659 17.6384628 0.0057368 3074.62 <2e-16 ***
DESTIN_SZ660 18.2538855 0.0040861 4467.32 <2e-16 ***
DESTIN_SZ662 16.9808432 0.0115807 1466.31 <2e-16 ***
DESTIN_SZ677 17.7386129 0.0092539 1916.89 <2e-16 ***
DESTIN_SZ678 16.1434356 0.0137714 1172.24 <2e-16 ***
DESTIN_SZ679 17.6987142 0.0049770 3556.13 <2e-16 ***
DESTIN_SZ680 19.5108225 0.0026778 7286.16 <2e-16 ***
DESTIN_SZ681 16.2941696 0.0175510 928.39 <2e-16 ***
DESTIN_SZ699 17.0802411 0.0089024 1918.61 <2e-16 ***
DESTIN_SZ700 17.3754689 0.0068593 2533.14 <2e-16 ***
DESTIN_SZ701 15.3904622 0.0191672 802.96 <2e-16 ***
DESTIN_SZ702 17.8741006 0.0046971 3805.34 <2e-16 ***
DESTIN_SZ704 17.3239918 0.0106139 1632.19 <2e-16 ***
DESTIN_SZ722 17.1982826 0.0087045 1975.80 <2e-16 ***
DESTIN_SZ725 15.6113259 0.0259626 601.30 <2e-16 ***
DESTIN_SZ741 17.6248992 0.0071347 2470.30 <2e-16 ***
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DESTIN_SZ1984 17.3040220 0.0061877 2796.50 <2e-16 ***
DESTIN_SZ1985 17.6967797 0.0058128 3044.44 <2e-16 ***
DESTIN_SZ2001 17.0599093 0.0065178 2617.43 <2e-16 ***
DESTIN_SZ2002 17.3903322 0.0050415 3449.47 <2e-16 ***
DESTIN_SZ2003 18.0518300 0.0043596 4140.68 <2e-16 ***
DESTIN_SZ2004 18.3363157 0.0041171 4453.68 <2e-16 ***
DESTIN_SZ2005 17.1532095 0.0063773 2689.73 <2e-16 ***
DESTIN_SZ2006 18.2144546 0.0046465 3920.01 <2e-16 ***
DESTIN_SZ2007 15.0407848 0.0296401 507.45 <2e-16 ***
DESTIN_SZ2022 17.6896037 0.0063981 2764.80 <2e-16 ***
DESTIN_SZ2023 17.8550645 0.0046104 3872.80 <2e-16 ***
DESTIN_SZ2024 18.1751126 0.0039777 4569.24 <2e-16 ***
DESTIN_SZ2025 17.1314917 0.0064363 2661.72 <2e-16 ***
DESTIN_SZ2026 16.3461928 0.0115865 1410.79 <2e-16 ***
DESTIN_SZ2027 18.0907515 0.0044046 4107.22 <2e-16 ***
DESTIN_SZ2043 16.2006762 0.0111394 1454.36 <2e-16 ***
DESTIN_SZ2044 17.2464964 0.0057305 3009.59 <2e-16 ***
DESTIN_SZ2045 16.7799564 0.0116939 1434.93 <2e-16 ***
DESTIN_SZ2046 18.2387337 0.0036676 4972.99 <2e-16 ***
DESTIN_SZ2047 16.5589614 0.0090044 1838.98 <2e-16 ***
DESTIN_SZ2048 16.6440793 0.0084165 1977.57 <2e-16 ***
DESTIN_SZ2049 14.9903280 0.0276919 541.33 <2e-16 ***
DESTIN_SZ2064 17.0500355 0.0069422 2455.99 <2e-16 ***
DESTIN_SZ2065 16.9370135 0.0070668 2396.70 <2e-16 ***
DESTIN_SZ2066 15.1753466 0.0324733 467.32 <2e-16 ***
DESTIN_SZ2067 19.5021151 0.0024554 7942.46 <2e-16 ***
DESTIN_SZ2068 16.6213149 0.0130997 1268.83 <2e-16 ***
DESTIN_SZ2069 16.8594945 0.0082006 2055.89 <2e-16 ***
DESTIN_SZ2085 17.0904490 0.0073605 2321.90 <2e-16 ***
DESTIN_SZ2086 18.2772357 0.0037498 4874.16 <2e-16 ***
DESTIN_SZ2087 18.0889350 0.0040279 4490.89 <2e-16 ***
DESTIN_SZ2088 17.3029530 0.0056087 3085.01 <2e-16 ***
DESTIN_SZ2089 17.0015397 0.0088051 1930.86 <2e-16 ***
DESTIN_SZ2090 19.1760482 0.0027444 6987.30 <2e-16 ***
DESTIN_SZ2091 14.0647667 0.0665418 211.37 <2e-16 ***
DESTIN_SZ2105 15.9401982 0.0636648 250.38 <2e-16 ***
DESTIN_SZ2106 15.5885926 0.0148891 1046.98 <2e-16 ***
DESTIN_SZ2107 18.2606668 0.0037141 4916.53 <2e-16 ***
DESTIN_SZ2108 18.0256039 0.0045837 3932.55 <2e-16 ***
DESTIN_SZ2109 17.0341340 0.0064513 2640.41 <2e-16 ***
DESTIN_SZ2110 16.4783325 0.0115616 1425.26 <2e-16 ***
DESTIN_SZ2111 15.1465446 0.0329430 459.78 <2e-16 ***
DESTIN_SZ2128 17.2202324 0.0082295 2092.51 <2e-16 ***
DESTIN_SZ2129 16.5528201 0.0098828 1674.91 <2e-16 ***
DESTIN_SZ2130 17.3476185 0.0053464 3244.73 <2e-16 ***
DESTIN_SZ2131 17.4105124 0.0069407 2508.48 <2e-16 ***
DESTIN_SZ2132 17.0130022 0.0074096 2296.07 <2e-16 ***
DESTIN_SZ2148 16.3085207 0.0146352 1114.34 <2e-16 ***
DESTIN_SZ2149 16.3982869 0.0108065 1517.45 <2e-16 ***
DESTIN_SZ2150 16.7223793 0.0081235 2058.51 <2e-16 ***
DESTIN_SZ2151 18.6217838 0.0031665 5880.87 <2e-16 ***
DESTIN_SZ2152 17.7368329 0.0050850 3488.08 <2e-16 ***
DESTIN_SZ2153 16.4151939 0.0111532 1471.79 <2e-16 ***
DESTIN_SZ2171 17.5000225 0.0054451 3213.91 <2e-16 ***
DESTIN_SZ2172 16.3172933 0.0109332 1492.45 <2e-16 ***
DESTIN_SZ2173 16.7742789 0.0072780 2304.78 <2e-16 ***
DESTIN_SZ2174 17.3302208 0.0065154 2659.90 <2e-16 ***
DESTIN_SZ2191 17.5527703 0.0073207 2397.67 <2e-16 ***
DESTIN_SZ2192 16.3931709 0.0107252 1528.47 <2e-16 ***
DESTIN_SZ2193 17.2515636 0.0063032 2736.94 <2e-16 ***
DESTIN_SZ2194 17.3483342 0.0056916 3048.04 <2e-16 ***
DESTIN_SZ2195 15.8344157 0.0354660 446.47 <2e-16 ***
DESTIN_SZ2212 17.5803345 0.0127446 1379.43 <2e-16 ***
DESTIN_SZ2213 17.3429779 0.0080955 2142.29 <2e-16 ***
DESTIN_SZ2214 18.0067877 0.0069758 2581.32 <2e-16 ***
DESTIN_SZ2215 16.4921760 0.0094232 1750.17 <2e-16 ***
DESTIN_SZ2216 17.5061556 0.0060488 2894.17 <2e-16 ***
DESTIN_SZ2233 18.1631439 0.0096552 1881.17 <2e-16 ***
DESTIN_SZ2234 18.2930066 0.0081262 2251.11 <2e-16 ***
DESTIN_SZ2235 17.2635477 0.0087521 1972.51 <2e-16 ***
DESTIN_SZ2236 16.0178504 0.0136219 1175.89 <2e-16 ***
DESTIN_SZ2237 16.8737028 0.0112997 1493.29 <2e-16 ***
DESTIN_SZ2256 17.3481627 0.0119974 1446.00 <2e-16 ***
DESTIN_SZ2257 14.8625823 0.0261906 567.48 <2e-16 ***
DESTIN_SZ2258 16.8838961 0.0073537 2295.97 <2e-16 ***
DESTIN_SZ2259 17.7783318 0.0102016 1742.70 <2e-16 ***
DESTIN_SZ2277 16.1709752 0.0255881 631.97 <2e-16 ***
DESTIN_SZ2278 16.2155661 0.0157684 1028.36 <2e-16 ***
DESTIN_SZ2279 16.9167526 0.0075457 2241.92 <2e-16 ***
DESTIN_SZ2280 15.3121609 0.0311673 491.29 <2e-16 ***
DESTIN_SZ2297 16.1713813 0.0185179 873.28 <2e-16 ***
DESTIN_SZ2300 15.8616765 0.0205042 773.58 <2e-16 ***
DESTIN_SZ2301 16.6383378 0.0098711 1685.55 <2e-16 ***
DESTIN_SZ2318 18.6841212 0.0057960 3223.60 <2e-16 ***
DESTIN_SZ2319 18.5967829 0.0052309 3555.19 <2e-16 ***
DESTIN_SZ2322 17.1295002 0.0091323 1875.71 <2e-16 ***
DESTIN_SZ2337 17.5512708 0.0152767 1148.89 <2e-16 ***
DESTIN_SZ2341 18.9567095 0.0051747 3663.34 <2e-16 ***
DESTIN_SZ2343 16.1664742 0.0128582 1257.29 <2e-16 ***
DESTIN_SZ2361 17.4875772 0.0092317 1894.30 <2e-16 ***
DESTIN_SZ2364 14.9083138 0.0295342 504.78 <2e-16 ***
DESTIN_SZ2379 16.6530440 0.0241213 690.39 <2e-16 ***
DESTIN_SZ2384 18.1613369 0.0066839 2717.16 <2e-16 ***
DESTIN_SZ2405 18.5765284 0.0048050 3866.10 <2e-16 ***
DESTIN_SZ2406 15.5243322 0.0235366 659.58 <2e-16 ***
DESTIN_SZ2426 17.9192434 0.0109187 1641.14 <2e-16 ***
DESTIN_SZ2427 18.1441130 0.0066972 2709.19 <2e-16 ***
DESTIN_SZ2505 18.1648361 0.0181967 998.25 <2e-16 ***
log(BUSINESS_num) NA NA NA NA
log(FB_num) NA NA NA NA
log(schools_num) NA NA NA NA
log(hdb_num) NA NA NA NA
log(entertn_num) NA NA NA NA
log(dist) -1.4618825 0.0002562 -5705.39 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 349181331 on 64962 degrees of freedom
Residual deviance: 45737568 on 64142 degrees of freedom
AIC: 46097578
Number of Fisher Scoring iterations: 89.4.4 Doubly constrained
dbcSIM <- glm(formula = MORNING_PEAK ~ ORIGIN_SZ + DESTIN_SZ + log(dist), family = poisson(link = "log"), data = inter_zonal_flow, na.action = na.exclude)the calculated R-squared is 0.5871965, indicating that the model accounts for approximately 58.72% of the variability in the observed MORNING_PEAK.
Code
CalcRSquared(dbcSIM$data$MORNING_PEAK, dbcSIM$fitted.values)[1] 0.5871965Code
dbcSIM$coefficients[1](Intercept)
14.78251 Code
dbcSIM$coefficients[1635]DESTIN_SZ2505
0.7094831 Code
options(max.print = 10000)
summary(dbcSIM)
Call:
glm(formula = MORNING_PEAK ~ ORIGIN_SZ + DESTIN_SZ + log(dist),
family = poisson(link = "log"), data = inter_zonal_flow,
na.action = na.exclude)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) 14.7825131 0.1376669 107.379 < 2e-16 ***
ORIGIN_SZ44 1.8651637 0.1913130 9.749 < 2e-16 ***
ORIGIN_SZ46 -0.4638760 0.1580502 -2.935 0.003336 **
ORIGIN_SZ66 0.8207510 0.1832131 4.480 7.47e-06 ***
ORIGIN_SZ67 1.7280743 0.1304829 13.244 < 2e-16 ***
ORIGIN_SZ68 -0.5924438 0.1696234 -3.493 0.000478 ***
ORIGIN_SZ86 -0.4088340 0.1503510 -2.719 0.006544 **
ORIGIN_SZ87 3.5035738 0.1480694 23.662 < 2e-16 ***
ORIGIN_SZ88 2.5215503 0.1292031 19.516 < 2e-16 ***
ORIGIN_SZ89 0.2300891 0.1375846 1.672 0.094456 .
ORIGIN_SZ90 1.0781361 0.1779172 6.060 1.36e-09 ***
ORIGIN_SZ109 0.6458122 0.1567823 4.119 3.80e-05 ***
ORIGIN_SZ110 0.6774575 0.1494445 4.533 5.81e-06 ***
ORIGIN_SZ111 4.0448044 0.1288315 31.396 < 2e-16 ***
ORIGIN_SZ112 0.1521353 0.1453988 1.046 0.295408
ORIGIN_SZ128 3.3585869 0.1312681 25.586 < 2e-16 ***
ORIGIN_SZ129 0.4780069 0.2187567 2.185 0.028881 *
ORIGIN_SZ130 1.4046878 0.1390554 10.102 < 2e-16 ***
ORIGIN_SZ131 1.1414313 0.1322103 8.633 < 2e-16 ***
ORIGIN_SZ132 0.2245551 0.1388237 1.618 0.105758
ORIGIN_SZ133 1.1920048 0.1344194 8.868 < 2e-16 ***
ORIGIN_SZ134 4.3098259 0.1312397 32.839 < 2e-16 ***
ORIGIN_SZ150 4.3536568 0.1297949 33.543 < 2e-16 ***
ORIGIN_SZ151 0.7972520 0.1445269 5.516 3.46e-08 ***
ORIGIN_SZ152 0.2520616 0.1527246 1.650 0.098855 .
ORIGIN_SZ153 1.6168138 0.1350720 11.970 < 2e-16 ***
ORIGIN_SZ154 4.2669539 0.1283580 33.243 < 2e-16 ***
ORIGIN_SZ155 1.2036839 0.1329298 9.055 < 2e-16 ***
ORIGIN_SZ156 2.1952570 0.1355002 16.201 < 2e-16 ***
ORIGIN_SZ172 2.4447822 0.1435353 17.033 < 2e-16 ***
ORIGIN_SZ174 1.1354702 0.1367109 8.306 < 2e-16 ***
ORIGIN_SZ175 3.8895209 0.1286409 30.235 < 2e-16 ***
ORIGIN_SZ176 4.9927160 0.1282428 38.932 < 2e-16 ***
ORIGIN_SZ195 0.1461498 0.1503134 0.972 0.330901
ORIGIN_SZ196 1.1205023 0.1339388 8.366 < 2e-16 ***
ORIGIN_SZ197 0.2039552 0.1785044 1.143 0.253214
ORIGIN_SZ215 1.7228934 0.1548747 11.124 < 2e-16 ***
ORIGIN_SZ216 5.3512021 0.1283651 41.687 < 2e-16 ***
ORIGIN_SZ217 2.4696949 0.1299800 19.001 < 2e-16 ***
ORIGIN_SZ237 -0.1148070 0.2104278 -0.546 0.585349
ORIGIN_SZ238 0.9871565 0.1467267 6.728 1.72e-11 ***
ORIGIN_SZ239 1.2506722 0.1870828 6.685 2.31e-11 ***
ORIGIN_SZ257 0.2715459 0.1408892 1.927 0.053933 .
ORIGIN_SZ258 2.2349763 0.1314398 17.004 < 2e-16 ***
ORIGIN_SZ259 1.6038725 0.1342585 11.946 < 2e-16 ***
ORIGIN_SZ278 1.8380732 0.1332248 13.797 < 2e-16 ***
ORIGIN_SZ279 0.6102791 0.1357349 4.496 6.92e-06 ***
ORIGIN_SZ280 1.0967209 0.1369188 8.010 1.15e-15 ***
ORIGIN_SZ298 -2.9525019 0.3573065 -8.263 < 2e-16 ***
ORIGIN_SZ299 0.4052485 0.1386668 2.922 0.003473 **
ORIGIN_SZ300 4.2242256 0.1285551 32.859 < 2e-16 ***
ORIGIN_SZ320 -0.1304437 0.1374289 -0.949 0.342533
ORIGIN_SZ321 1.0223496 0.1486339 6.878 6.06e-12 ***
ORIGIN_SZ322 2.1303020 0.1344205 15.848 < 2e-16 ***
ORIGIN_SZ340 1.7776512 0.1312870 13.540 < 2e-16 ***
ORIGIN_SZ341 0.1698864 0.1359914 1.249 0.211576
ORIGIN_SZ342 2.0446107 0.1344315 15.209 < 2e-16 ***
ORIGIN_SZ363 1.7399036 0.1336962 13.014 < 2e-16 ***
ORIGIN_SZ364 2.2324348 0.1310346 17.037 < 2e-16 ***
ORIGIN_SZ383 1.2662322 0.1319317 9.598 < 2e-16 ***
ORIGIN_SZ384 0.4729125 0.1372673 3.445 0.000571 ***
ORIGIN_SZ385 1.6732365 0.1364878 12.259 < 2e-16 ***
ORIGIN_SZ404 2.2671817 0.1316880 17.216 < 2e-16 ***
ORIGIN_SZ405 0.6452881 0.1382800 4.667 3.06e-06 ***
ORIGIN_SZ406 6.0984179 0.1282803 47.540 < 2e-16 ***
ORIGIN_SZ407 2.3074859 0.1341287 17.204 < 2e-16 ***
ORIGIN_SZ408 3.0326485 0.1298347 23.358 < 2e-16 ***
ORIGIN_SZ425 -0.4946901 0.1608092 -3.076 0.002096 **
ORIGIN_SZ426 1.5311039 0.1318184 11.615 < 2e-16 ***
ORIGIN_SZ427 0.9190448 0.1350628 6.805 1.01e-11 ***
ORIGIN_SZ428 1.0913201 0.1480848 7.370 1.71e-13 ***
ORIGIN_SZ429 2.5227525 0.1294959 19.481 < 2e-16 ***
ORIGIN_SZ446 1.4303619 0.1412628 10.126 < 2e-16 ***
ORIGIN_SZ447 0.7386870 0.1344585 5.494 3.93e-08 ***
ORIGIN_SZ448 1.9352844 0.1310960 14.762 < 2e-16 ***
ORIGIN_SZ449 5.2559562 0.1284385 40.922 < 2e-16 ***
ORIGIN_SZ450 2.2474602 0.1294904 17.356 < 2e-16 ***
ORIGIN_SZ468 1.9333540 0.1318865 14.659 < 2e-16 ***
ORIGIN_SZ469 3.1703947 0.1291647 24.545 < 2e-16 ***
ORIGIN_SZ470 5.2270506 0.1283788 40.716 < 2e-16 ***
ORIGIN_SZ471 3.2081727 0.1291587 24.839 < 2e-16 ***
ORIGIN_SZ488 0.8657735 0.1398141 6.192 5.93e-10 ***
ORIGIN_SZ489 -0.8857821 0.2053213 -4.314 1.60e-05 ***
ORIGIN_SZ490 3.6851496 0.1288719 28.595 < 2e-16 ***
ORIGIN_SZ491 4.1880606 0.1285170 32.588 < 2e-16 ***
ORIGIN_SZ493 -1.1749485 0.2122468 -5.536 3.10e-08 ***
ORIGIN_SZ494 1.2353383 0.1428587 8.647 < 2e-16 ***
ORIGIN_SZ509 0.7461932 0.1334786 5.590 2.27e-08 ***
ORIGIN_SZ510 1.5711689 0.1308049 12.012 < 2e-16 ***
ORIGIN_SZ511 3.1384338 0.1287544 24.375 < 2e-16 ***
ORIGIN_SZ512 5.8131536 0.1283280 45.299 < 2e-16 ***
ORIGIN_SZ513 2.3201534 0.1306174 17.763 < 2e-16 ***
ORIGIN_SZ514 2.1168213 0.1340983 15.786 < 2e-16 ***
ORIGIN_SZ515 0.3959269 0.1995066 1.985 0.047197 *
ORIGIN_SZ530 -0.1051997 0.1551347 -0.678 0.497697
ORIGIN_SZ531 2.1354352 0.1298169 16.450 < 2e-16 ***
ORIGIN_SZ532 1.5154353 0.1307571 11.590 < 2e-16 ***
ORIGIN_SZ533 5.5870356 0.1283265 43.538 < 2e-16 ***
ORIGIN_SZ534 6.1313157 0.1283403 47.774 < 2e-16 ***
ORIGIN_SZ536 2.8040298 0.1308424 21.431 < 2e-16 ***
ORIGIN_SZ537 0.9009629 0.1773825 5.079 3.79e-07 ***
ORIGIN_SZ538 0.7319978 0.2448586 2.989 0.002795 **
ORIGIN_SZ539 0.1889885 1.0087880 0.187 0.851392
ORIGIN_SZ551 -0.0802166 0.1389218 -0.577 0.563654
ORIGIN_SZ552 2.3580939 0.1334290 17.673 < 2e-16 ***
ORIGIN_SZ553 1.9548006 0.1294728 15.098 < 2e-16 ***
ORIGIN_SZ554 5.4436879 0.1283357 42.418 < 2e-16 ***
ORIGIN_SZ555 4.7990556 0.1284894 37.350 < 2e-16 ***
ORIGIN_SZ559 1.3434072 0.1615223 8.317 < 2e-16 ***
ORIGIN_SZ560 3.7651027 0.1360404 27.676 < 2e-16 ***
ORIGIN_SZ561 -1.3562021 1.0094990 -1.343 0.179129
ORIGIN_SZ572 -1.8802721 0.4282239 -4.391 1.13e-05 ***
ORIGIN_SZ573 0.4595648 0.1350553 3.403 0.000667 ***
ORIGIN_SZ574 1.8237630 0.1334734 13.664 < 2e-16 ***
ORIGIN_SZ575 6.5891046 0.1283083 51.354 < 2e-16 ***
ORIGIN_SZ576 5.0716420 0.1283839 39.504 < 2e-16 ***
ORIGIN_SZ578 0.3477660 0.1612539 2.157 0.031034 *
ORIGIN_SZ582 0.7041518 0.1661964 4.237 2.27e-05 ***
ORIGIN_SZ583 0.6990335 0.4279531 1.633 0.102378
ORIGIN_SZ584 4.2195182 0.1384317 30.481 < 2e-16 ***
ORIGIN_SZ593 1.5726840 0.1370901 11.472 < 2e-16 ***
ORIGIN_SZ594 1.5817148 0.1308139 12.091 < 2e-16 ***
ORIGIN_SZ595 1.8243274 0.1296637 14.070 < 2e-16 ***
ORIGIN_SZ596 4.8396880 0.1283597 37.704 < 2e-16 ***
ORIGIN_SZ597 2.0869369 0.1405580 14.848 < 2e-16 ***
ORIGIN_SZ603 1.3234042 0.1692391 7.820 5.29e-15 ***
ORIGIN_SZ604 1.7550673 0.2231652 7.864 3.71e-15 ***
ORIGIN_SZ615 0.2206062 0.1363140 1.618 0.105583
ORIGIN_SZ616 1.2829325 0.1320936 9.712 < 2e-16 ***
ORIGIN_SZ617 2.1648199 0.1295708 16.708 < 2e-16 ***
ORIGIN_SZ618 5.5155910 0.1283468 42.974 < 2e-16 ***
ORIGIN_SZ620 2.6761751 0.1317617 20.311 < 2e-16 ***
ORIGIN_SZ637 1.0365392 0.1348394 7.687 1.50e-14 ***
ORIGIN_SZ638 4.9647838 0.1283593 38.679 < 2e-16 ***
ORIGIN_SZ657 2.8464046 0.1293749 22.001 < 2e-16 ***
ORIGIN_SZ658 4.3118367 0.1284518 33.568 < 2e-16 ***
ORIGIN_SZ659 4.5165384 0.1284061 35.174 < 2e-16 ***
ORIGIN_SZ660 5.6795444 0.1283370 44.255 < 2e-16 ***
ORIGIN_SZ662 5.6490277 0.1285159 43.956 < 2e-16 ***
ORIGIN_SZ677 2.7261064 0.1302955 20.922 < 2e-16 ***
ORIGIN_SZ678 0.5485599 0.1364948 4.019 5.85e-05 ***
ORIGIN_SZ679 5.5476455 0.1283465 43.224 < 2e-16 ***
ORIGIN_SZ680 5.7814553 0.1283449 45.046 < 2e-16 ***
ORIGIN_SZ681 4.4894509 0.1285630 34.920 < 2e-16 ***
ORIGIN_SZ699 2.2405240 0.1302647 17.200 < 2e-16 ***
ORIGIN_SZ700 4.4925825 0.1284369 34.979 < 2e-16 ***
ORIGIN_SZ701 4.4095803 0.1284380 34.332 < 2e-16 ***
ORIGIN_SZ702 5.4786781 0.1283432 42.688 < 2e-16 ***
ORIGIN_SZ704 2.5640128 0.1322083 19.394 < 2e-16 ***
ORIGIN_SZ722 2.2596147 0.1295939 17.436 < 2e-16 ***
ORIGIN_SZ725 2.0324175 0.1345148 15.109 < 2e-16 ***
ORIGIN_SZ741 2.7762245 0.1293588 21.461 < 2e-16 ***
ORIGIN_SZ743 2.9902364 0.1288881 23.200 < 2e-16 ***
ORIGIN_SZ744 5.0780767 0.1283722 39.557 < 2e-16 ***
ORIGIN_SZ761 2.3192045 0.1312756 17.667 < 2e-16 ***
ORIGIN_SZ762 4.2846462 0.1285059 33.342 < 2e-16 ***
ORIGIN_SZ763 1.5206569 0.1310794 11.601 < 2e-16 ***
ORIGIN_SZ764 5.5790146 0.1283416 43.470 < 2e-16 ***
ORIGIN_SZ765 4.7777270 0.1285630 37.163 < 2e-16 ***
ORIGIN_SZ767 6.6070303 0.1283571 51.474 < 2e-16 ***
ORIGIN_SZ772 1.3281976 0.1484396 8.948 < 2e-16 ***
ORIGIN_SZ784 1.3670047 0.1310123 10.434 < 2e-16 ***
ORIGIN_SZ785 4.6756446 0.1283700 36.423 < 2e-16 ***
ORIGIN_SZ786 4.3556867 0.1284389 33.913 < 2e-16 ***
ORIGIN_SZ787 4.9407778 0.1285040 38.448 < 2e-16 ***
ORIGIN_SZ788 5.7989893 0.1284141 45.159 < 2e-16 ***
ORIGIN_SZ789 4.2570120 0.1287218 33.071 < 2e-16 ***
ORIGIN_SZ803 0.5015402 0.1388696 3.612 0.000304 ***
ORIGIN_SZ804 5.3266445 0.1283676 41.495 < 2e-16 ***
ORIGIN_SZ805 5.2948963 0.1283446 41.255 < 2e-16 ***
ORIGIN_SZ806 5.0165155 0.1283678 39.079 < 2e-16 ***
ORIGIN_SZ807 6.0112348 0.1283728 46.826 < 2e-16 ***
ORIGIN_SZ808 4.2397833 0.1287592 32.928 < 2e-16 ***
ORIGIN_SZ809 6.0018355 0.1283491 46.762 < 2e-16 ***
ORIGIN_SZ810 5.2248926 0.1284356 40.681 < 2e-16 ***
ORIGIN_SZ814 3.1415033 0.1311682 23.950 < 2e-16 ***
ORIGIN_SZ819 5.2782677 0.1295641 40.739 < 2e-16 ***
ORIGIN_SZ824 1.4838427 0.1338729 11.084 < 2e-16 ***
ORIGIN_SZ826 2.9697079 0.1286813 23.078 < 2e-16 ***
ORIGIN_SZ827 4.9601290 0.1283584 38.643 < 2e-16 ***
ORIGIN_SZ828 5.3539759 0.1283522 41.713 < 2e-16 ***
ORIGIN_SZ829 5.4057517 0.1283801 42.107 < 2e-16 ***
ORIGIN_SZ830 5.6207518 0.1284042 43.774 < 2e-16 ***
ORIGIN_SZ831 6.5320399 0.1283357 50.898 < 2e-16 ***
ORIGIN_SZ832 5.6900053 0.1284630 44.293 < 2e-16 ***
ORIGIN_SZ835 3.0146096 0.1315282 22.920 < 2e-16 ***
ORIGIN_SZ844 0.4681830 0.1482345 3.158 0.001586 **
ORIGIN_SZ846 4.3998432 0.1284074 34.265 < 2e-16 ***
ORIGIN_SZ847 3.5040945 0.1286150 27.245 < 2e-16 ***
ORIGIN_SZ848 4.7250679 0.1283870 36.803 < 2e-16 ***
ORIGIN_SZ849 3.9550633 0.1285238 30.773 < 2e-16 ***
ORIGIN_SZ850 4.8690494 0.1284142 37.917 < 2e-16 ***
ORIGIN_SZ851 5.4253340 0.1283676 42.264 < 2e-16 ***
ORIGIN_SZ852 4.9548384 0.1284522 38.573 < 2e-16 ***
ORIGIN_SZ853 6.9365719 0.1283778 54.032 < 2e-16 ***
ORIGIN_SZ854 3.2237110 0.1308010 24.646 < 2e-16 ***
ORIGIN_SZ855 1.8416130 0.1353800 13.603 < 2e-16 ***
ORIGIN_SZ856 3.4683981 0.1296780 26.746 < 2e-16 ***
ORIGIN_SZ866 2.3172711 0.1310822 17.678 < 2e-16 ***
ORIGIN_SZ867 3.1976249 0.1288244 24.822 < 2e-16 ***
ORIGIN_SZ868 2.4882976 0.1294932 19.216 < 2e-16 ***
ORIGIN_SZ869 5.0233449 0.1284450 39.109 < 2e-16 ***
ORIGIN_SZ870 5.9104196 0.1283334 46.055 < 2e-16 ***
ORIGIN_SZ871 5.7459917 0.1284312 44.740 < 2e-16 ***
ORIGIN_SZ872 3.6190123 0.1287687 28.105 < 2e-16 ***
ORIGIN_SZ873 3.8506553 0.1286792 29.924 < 2e-16 ***
ORIGIN_SZ874 4.1234873 0.1285464 32.078 < 2e-16 ***
ORIGIN_SZ875 1.0949378 0.1438786 7.610 2.74e-14 ***
ORIGIN_SZ876 2.2269604 0.1318447 16.891 < 2e-16 ***
ORIGIN_SZ877 1.7867469 0.1341387 13.320 < 2e-16 ***
ORIGIN_SZ887 2.6306026 0.1289823 20.395 < 2e-16 ***
ORIGIN_SZ888 4.1253397 0.1284797 32.109 < 2e-16 ***
ORIGIN_SZ889 1.0535960 0.1320251 7.980 1.46e-15 ***
ORIGIN_SZ890 5.3284587 0.1283518 41.514 < 2e-16 ***
ORIGIN_SZ891 4.0268547 0.1287780 31.270 < 2e-16 ***
ORIGIN_SZ893 5.4681295 0.1283613 42.600 < 2e-16 ***
ORIGIN_SZ894 3.6741126 0.1287171 28.544 < 2e-16 ***
ORIGIN_SZ895 3.1918333 0.1291808 24.708 < 2e-16 ***
ORIGIN_SZ896 1.9784262 0.1315361 15.041 < 2e-16 ***
ORIGIN_SZ897 0.3264987 0.1420392 2.299 0.021525 *
ORIGIN_SZ898 2.5017205 0.1320423 18.946 < 2e-16 ***
ORIGIN_SZ908 4.1028770 0.1288535 31.841 < 2e-16 ***
ORIGIN_SZ909 4.1157508 0.1284197 32.049 < 2e-16 ***
ORIGIN_SZ910 2.1546228 0.1293238 16.661 < 2e-16 ***
ORIGIN_SZ911 3.5439302 0.1285925 27.559 < 2e-16 ***
ORIGIN_SZ912 5.0794681 0.1283673 39.570 < 2e-16 ***
ORIGIN_SZ915 5.3722279 0.1283714 41.849 < 2e-16 ***
ORIGIN_SZ917 4.8669273 0.1285088 37.872 < 2e-16 ***
ORIGIN_SZ918 1.1976582 0.1338619 8.947 < 2e-16 ***
ORIGIN_SZ919 4.1125271 0.1286438 31.968 < 2e-16 ***
ORIGIN_SZ928 3.0455756 0.1289702 23.615 < 2e-16 ***
ORIGIN_SZ929 4.4978222 0.1283770 35.036 < 2e-16 ***
ORIGIN_SZ930 5.3657820 0.1283355 41.811 < 2e-16 ***
ORIGIN_SZ931 2.3162035 0.1293690 17.904 < 2e-16 ***
ORIGIN_SZ932 2.7694625 0.1294770 21.390 < 2e-16 ***
ORIGIN_SZ933 4.9357933 0.1284184 38.435 < 2e-16 ***
ORIGIN_SZ934 2.3306921 0.1296816 17.972 < 2e-16 ***
ORIGIN_SZ935 6.2496853 0.1283348 48.698 < 2e-16 ***
ORIGIN_SZ938 -1.6147369 0.2810424 -5.746 9.16e-09 ***
ORIGIN_SZ939 6.2324982 0.1283674 48.552 < 2e-16 ***
ORIGIN_SZ940 0.4374257 0.1465384 2.985 0.002835 **
ORIGIN_SZ949 2.7913292 0.1289455 21.647 < 2e-16 ***
ORIGIN_SZ950 4.9625752 0.1283901 38.652 < 2e-16 ***
ORIGIN_SZ951 5.8124044 0.1283280 45.293 < 2e-16 ***
ORIGIN_SZ952 2.5331222 0.1298464 19.509 < 2e-16 ***
ORIGIN_SZ953 3.7049359 0.1286368 28.802 < 2e-16 ***
ORIGIN_SZ954 2.5590881 0.1293518 19.784 < 2e-16 ***
ORIGIN_SZ955 4.8206888 0.1284189 37.539 < 2e-16 ***
ORIGIN_SZ956 3.2253869 0.1287870 25.044 < 2e-16 ***
ORIGIN_SZ957 5.3750668 0.1284242 41.854 < 2e-16 ***
ORIGIN_SZ959 1.4277296 0.1368777 10.431 < 2e-16 ***
ORIGIN_SZ961 1.4545836 0.1317928 11.037 < 2e-16 ***
ORIGIN_SZ962 6.7795777 0.1284728 52.771 < 2e-16 ***
ORIGIN_SZ970 3.3200875 0.1285368 25.830 < 2e-16 ***
ORIGIN_SZ971 4.6872948 0.1283546 36.518 < 2e-16 ***
ORIGIN_SZ972 4.5754058 0.1283801 35.640 < 2e-16 ***
ORIGIN_SZ974 4.2151790 0.1284972 32.804 < 2e-16 ***
ORIGIN_SZ975 3.8529613 0.1285929 29.962 < 2e-16 ***
ORIGIN_SZ976 2.5736286 0.1293162 19.902 < 2e-16 ***
ORIGIN_SZ977 5.7393499 0.1283528 44.715 < 2e-16 ***
ORIGIN_SZ978 5.6271784 0.1284820 43.797 < 2e-16 ***
ORIGIN_SZ982 2.5287621 0.1291557 19.579 < 2e-16 ***
ORIGIN_SZ983 7.4453499 0.1283646 58.002 < 2e-16 ***
ORIGIN_SZ984 7.4937210 0.1283984 58.363 < 2e-16 ***
ORIGIN_SZ991 3.3688268 0.1285932 26.198 < 2e-16 ***
ORIGIN_SZ992 3.6566784 0.1284744 28.462 < 2e-16 ***
ORIGIN_SZ993 3.4070732 0.1285045 26.513 < 2e-16 ***
ORIGIN_SZ994 2.9499187 0.1287275 22.916 < 2e-16 ***
ORIGIN_SZ995 4.3993511 0.1284162 34.259 < 2e-16 ***
ORIGIN_SZ996 4.1139306 0.1285169 32.011 < 2e-16 ***
ORIGIN_SZ997 2.8308973 0.1311854 21.579 < 2e-16 ***
ORIGIN_SZ998 5.8555628 0.1283574 45.619 < 2e-16 ***
ORIGIN_SZ999 5.8385828 0.1284204 45.465 < 2e-16 ***
ORIGIN_SZ1001 2.6713211 0.1306592 20.445 < 2e-16 ***
ORIGIN_SZ1003 5.3580592 0.1283740 41.738 < 2e-16 ***
ORIGIN_SZ1004 6.0074265 0.1283503 46.805 < 2e-16 ***
ORIGIN_SZ1011 1.3614625 0.1319247 10.320 < 2e-16 ***
ORIGIN_SZ1012 1.3964150 0.1321703 10.565 < 2e-16 ***
ORIGIN_SZ1013 2.1051864 0.1293209 16.279 < 2e-16 ***
ORIGIN_SZ1014 2.9620901 0.1287294 23.010 < 2e-16 ***
ORIGIN_SZ1015 2.4138370 0.1291886 18.685 < 2e-16 ***
ORIGIN_SZ1016 4.1555792 0.1284861 32.343 < 2e-16 ***
ORIGIN_SZ1018 4.7337897 0.1286573 36.794 < 2e-16 ***
ORIGIN_SZ1019 6.3123786 0.1283874 49.167 < 2e-16 ***
ORIGIN_SZ1023 4.3697894 0.1286306 33.972 < 2e-16 ***
ORIGIN_SZ1024 5.3946861 0.1283850 42.020 < 2e-16 ***
ORIGIN_SZ1025 0.5797077 0.1378446 4.206 2.60e-05 ***
ORIGIN_SZ1033 2.7628241 0.1287715 21.455 < 2e-16 ***
ORIGIN_SZ1034 3.7076914 0.1284935 28.855 < 2e-16 ***
ORIGIN_SZ1035 4.4197167 0.1284092 34.419 < 2e-16 ***
ORIGIN_SZ1036 2.4413074 0.1291227 18.907 < 2e-16 ***
ORIGIN_SZ1037 3.6810703 0.1284912 28.648 < 2e-16 ***
ORIGIN_SZ1043 2.7041178 0.1306722 20.694 < 2e-16 ***
ORIGIN_SZ1045 5.0036359 0.1283827 38.974 < 2e-16 ***
ORIGIN_SZ1046 4.8600249 0.1284019 37.850 < 2e-16 ***
ORIGIN_SZ1053 4.2805812 0.1284235 33.332 < 2e-16 ***
ORIGIN_SZ1054 3.1721677 0.1285584 24.675 < 2e-16 ***
ORIGIN_SZ1055 4.3164605 0.1284015 33.617 < 2e-16 ***
ORIGIN_SZ1056 3.3449664 0.1286159 26.007 < 2e-16 ***
ORIGIN_SZ1064 0.3641541 0.2684429 1.357 0.174927
ORIGIN_SZ1066 4.7807553 0.1284028 37.232 < 2e-16 ***
ORIGIN_SZ1067 5.5362003 0.1284055 43.115 < 2e-16 ***
ORIGIN_SZ1074 3.6129635 0.1285148 28.113 < 2e-16 ***
ORIGIN_SZ1075 2.8313889 0.1287176 21.997 < 2e-16 ***
ORIGIN_SZ1076 3.0018657 0.1285817 23.346 < 2e-16 ***
ORIGIN_SZ1077 3.2299883 0.1286726 25.102 < 2e-16 ***
ORIGIN_SZ1079 4.6158888 0.1284070 35.947 < 2e-16 ***
ORIGIN_SZ1085 -1.6741102 0.2142978 -7.812 5.63e-15 ***
ORIGIN_SZ1087 4.5588996 0.1284355 35.496 < 2e-16 ***
ORIGIN_SZ1088 3.0334034 0.1288400 23.544 < 2e-16 ***
ORIGIN_SZ1094 1.6330476 0.1355237 12.050 < 2e-16 ***
ORIGIN_SZ1095 1.0000862 0.1337777 7.476 7.68e-14 ***
ORIGIN_SZ1096 2.9821904 0.1298896 22.959 < 2e-16 ***
ORIGIN_SZ1097 5.0906615 0.1283501 39.662 < 2e-16 ***
ORIGIN_SZ1098 2.6108029 0.1295066 20.160 < 2e-16 ***
ORIGIN_SZ1099 4.0158899 0.1284725 31.259 < 2e-16 ***
ORIGIN_SZ1105 1.7724246 0.1429485 12.399 < 2e-16 ***
ORIGIN_SZ1106 0.0153603 0.1613298 0.095 0.924147
ORIGIN_SZ1107 2.3455815 0.1314244 17.847 < 2e-16 ***
ORIGIN_SZ1108 6.6047138 0.1283347 51.465 < 2e-16 ***
ORIGIN_SZ1109 3.9159747 0.1285455 30.464 < 2e-16 ***
ORIGIN_SZ1116 3.3236220 0.1285814 25.848 < 2e-16 ***
ORIGIN_SZ1117 1.7078013 0.1298638 13.151 < 2e-16 ***
ORIGIN_SZ1118 2.2710221 0.1295121 17.535 < 2e-16 ***
ORIGIN_SZ1119 3.2002136 0.1286806 24.869 < 2e-16 ***
ORIGIN_SZ1120 3.1584771 0.1289782 24.488 < 2e-16 ***
ORIGIN_SZ1129 5.0437158 0.1283974 39.282 < 2e-16 ***
ORIGIN_SZ1130 5.0856121 0.1283706 39.617 < 2e-16 ***
ORIGIN_SZ1131 4.4503068 0.1285519 34.619 < 2e-16 ***
ORIGIN_SZ1136 2.3574337 0.1290568 18.267 < 2e-16 ***
ORIGIN_SZ1138 0.9244841 0.1329645 6.953 3.58e-12 ***
ORIGIN_SZ1139 4.1524155 0.1284025 32.339 < 2e-16 ***
ORIGIN_SZ1141 4.1071977 0.1284565 31.973 < 2e-16 ***
ORIGIN_SZ1148 1.4188214 0.1384438 10.248 < 2e-16 ***
ORIGIN_SZ1149 2.9120967 0.1295611 22.477 < 2e-16 ***
ORIGIN_SZ1150 5.3044536 0.1283620 41.324 < 2e-16 ***
ORIGIN_SZ1151 4.2082018 0.1284711 32.756 < 2e-16 ***
ORIGIN_SZ1158 2.4313623 0.1287944 18.878 < 2e-16 ***
ORIGIN_SZ1159 3.9526476 0.1284212 30.779 < 2e-16 ***
ORIGIN_SZ1160 5.0104849 0.1283551 39.036 < 2e-16 ***
ORIGIN_SZ1171 5.8886025 0.1283717 45.871 < 2e-16 ***
ORIGIN_SZ1172 5.7411405 0.1283679 44.724 < 2e-16 ***
ORIGIN_SZ1173 2.8533942 0.1289138 22.134 < 2e-16 ***
ORIGIN_SZ1174 -1.6985984 0.2810566 -6.044 1.51e-09 ***
ORIGIN_SZ1178 2.7134960 0.1287189 21.081 < 2e-16 ***
ORIGIN_SZ1179 3.4454647 0.1284786 26.817 < 2e-16 ***
ORIGIN_SZ1180 4.5102659 0.1283724 35.134 < 2e-16 ***
ORIGIN_SZ1181 3.7584689 0.1284648 29.257 < 2e-16 ***
ORIGIN_SZ1183 2.8685027 0.1289376 22.247 < 2e-16 ***
ORIGIN_SZ1190 1.7003948 0.1368713 12.423 < 2e-16 ***
ORIGIN_SZ1192 4.6055665 0.1284622 35.852 < 2e-16 ***
ORIGIN_SZ1193 4.5964427 0.1284207 35.792 < 2e-16 ***
ORIGIN_SZ1194 2.8688838 0.1290323 22.234 < 2e-16 ***
ORIGIN_SZ1200 3.4689356 0.1284773 27.000 < 2e-16 ***
ORIGIN_SZ1201 3.3471765 0.1284958 26.049 < 2e-16 ***
ORIGIN_SZ1203 4.2403472 0.1284332 33.016 < 2e-16 ***
ORIGIN_SZ1204 3.9834418 0.1284700 31.007 < 2e-16 ***
ORIGIN_SZ1211 0.8732171 0.1653877 5.280 1.29e-07 ***
ORIGIN_SZ1214 5.3665337 0.1283778 41.803 < 2e-16 ***
ORIGIN_SZ1215 1.8296668 0.1344457 13.609 < 2e-16 ***
ORIGIN_SZ1216 0.9200164 0.1344061 6.845 7.64e-12 ***
ORIGIN_SZ1220 4.5147297 0.1283703 35.170 < 2e-16 ***
ORIGIN_SZ1221 4.1647047 0.1283842 32.439 < 2e-16 ***
ORIGIN_SZ1222 3.7853159 0.1286620 29.421 < 2e-16 ***
ORIGIN_SZ1223 2.1485159 0.1293868 16.605 < 2e-16 ***
ORIGIN_SZ1224 3.0637462 0.1287171 23.802 < 2e-16 ***
ORIGIN_SZ1231 -0.5785710 0.1931693 -2.995 0.002743 **
ORIGIN_SZ1232 1.6020338 0.1577109 10.158 < 2e-16 ***
ORIGIN_SZ1235 2.8891562 0.1290306 22.391 < 2e-16 ***
ORIGIN_SZ1236 2.6706813 0.1291650 20.677 < 2e-16 ***
ORIGIN_SZ1241 2.6749712 0.1287175 20.782 < 2e-16 ***
ORIGIN_SZ1242 3.3558722 0.1284773 26.120 < 2e-16 ***
ORIGIN_SZ1243 4.0336892 0.1283948 31.416 < 2e-16 ***
ORIGIN_SZ1246 3.2552150 0.1286250 25.308 < 2e-16 ***
ORIGIN_SZ1256 4.2865697 0.1285178 33.354 < 2e-16 ***
ORIGIN_SZ1257 5.1521683 0.1284247 40.118 < 2e-16 ***
ORIGIN_SZ1258 3.1495727 0.1290847 24.399 < 2e-16 ***
ORIGIN_SZ1262 3.0838272 0.1285660 23.986 < 2e-16 ***
ORIGIN_SZ1263 3.6926366 0.1284114 28.756 < 2e-16 ***
ORIGIN_SZ1264 2.6701258 0.1288620 20.721 < 2e-16 ***
ORIGIN_SZ1265 2.4338921 0.1291175 18.850 < 2e-16 ***
ORIGIN_SZ1266 3.8381859 0.1285277 29.863 < 2e-16 ***
ORIGIN_SZ1267 1.9652566 0.1309093 15.012 < 2e-16 ***
ORIGIN_SZ1272 -0.6005707 0.1784891 -3.365 0.000766 ***
ORIGIN_SZ1273 3.7329503 0.1288496 28.971 < 2e-16 ***
ORIGIN_SZ1277 5.3300196 0.1283783 41.518 < 2e-16 ***
ORIGIN_SZ1278 2.7968417 0.1289899 21.683 < 2e-16 ***
ORIGIN_SZ1283 4.9383464 0.1283620 38.472 < 2e-16 ***
ORIGIN_SZ1284 4.0964869 0.1283938 31.906 < 2e-16 ***
ORIGIN_SZ1285 4.8056051 0.1283510 37.441 < 2e-16 ***
ORIGIN_SZ1286 3.0869296 0.1286914 23.987 < 2e-16 ***
ORIGIN_SZ1289 1.3410831 0.1362765 9.841 < 2e-16 ***
ORIGIN_SZ1293 0.3168305 0.1480128 2.141 0.032309 *
ORIGIN_SZ1294 5.1414463 0.1284542 40.026 < 2e-16 ***
ORIGIN_SZ1295 2.6145693 0.1299450 20.121 < 2e-16 ***
ORIGIN_SZ1298 4.3456426 0.1284881 33.821 < 2e-16 ***
ORIGIN_SZ1299 4.5959685 0.1284570 35.778 < 2e-16 ***
ORIGIN_SZ1304 4.7072140 0.1283653 36.670 < 2e-16 ***
ORIGIN_SZ1305 4.1335815 0.1283719 32.200 < 2e-16 ***
ORIGIN_SZ1307 0.7500065 0.1331626 5.632 1.78e-08 ***
ORIGIN_SZ1308 3.9720413 0.1284550 30.922 < 2e-16 ***
ORIGIN_SZ1310 -0.7703709 0.2141972 -3.597 0.000322 ***
ORIGIN_SZ1316 1.5467810 0.1329477 11.635 < 2e-16 ***
ORIGIN_SZ1317 3.3278269 0.1288029 25.837 < 2e-16 ***
ORIGIN_SZ1318 2.6193558 0.1292355 20.268 < 2e-16 ***
ORIGIN_SZ1319 5.5800661 0.1283719 43.468 < 2e-16 ***
ORIGIN_SZ1320 4.0232570 0.1286368 31.276 < 2e-16 ***
ORIGIN_SZ1325 2.3380308 0.1288702 18.143 < 2e-16 ***
ORIGIN_SZ1326 4.3044463 0.1283701 33.532 < 2e-16 ***
ORIGIN_SZ1327 4.1268654 0.1283838 32.145 < 2e-16 ***
ORIGIN_SZ1328 2.7620098 0.1286476 21.470 < 2e-16 ***
ORIGIN_SZ1329 3.0506402 0.1288063 23.684 < 2e-16 ***
ORIGIN_SZ1330 3.8621532 0.1285638 30.041 < 2e-16 ***
ORIGIN_SZ1331 -1.2440279 0.2810167 -4.427 9.56e-06 ***
ORIGIN_SZ1333 3.2282984 0.1288720 25.050 < 2e-16 ***
ORIGIN_SZ1334 3.5087803 0.1287888 27.244 < 2e-16 ***
ORIGIN_SZ1335 3.0465284 0.1293834 23.547 < 2e-16 ***
ORIGIN_SZ1336 0.3602739 0.1726290 2.087 0.036890 *
ORIGIN_SZ1337 0.6865751 0.1381481 4.970 6.70e-07 ***
ORIGIN_SZ1338 -0.7332450 0.1603972 -4.571 4.84e-06 ***
ORIGIN_SZ1339 5.4952331 0.1283654 42.809 < 2e-16 ***
ORIGIN_SZ1340 3.8240135 0.1286071 29.734 < 2e-16 ***
ORIGIN_SZ1341 -0.1184385 0.2411330 -0.491 0.623303
ORIGIN_SZ1346 3.9045805 0.1284569 30.396 < 2e-16 ***
ORIGIN_SZ1347 4.9832894 0.1283510 38.825 < 2e-16 ***
ORIGIN_SZ1348 3.3585153 0.1284571 26.145 < 2e-16 ***
ORIGIN_SZ1349 3.1967346 0.1285549 24.867 < 2e-16 ***
ORIGIN_SZ1350 3.4336485 0.1287568 26.668 < 2e-16 ***
ORIGIN_SZ1353 3.5775524 0.1285755 27.825 < 2e-16 ***
ORIGIN_SZ1354 2.9970965 0.1289125 23.249 < 2e-16 ***
ORIGIN_SZ1355 3.8129551 0.1285760 29.655 < 2e-16 ***
ORIGIN_SZ1357 2.8838085 0.1296157 22.249 < 2e-16 ***
ORIGIN_SZ1358 4.2012475 0.1285152 32.691 < 2e-16 ***
ORIGIN_SZ1359 4.5175512 0.1284159 35.179 < 2e-16 ***
ORIGIN_SZ1360 4.5560472 0.1284234 35.477 < 2e-16 ***
ORIGIN_SZ1361 5.7082420 0.1283801 44.464 < 2e-16 ***
ORIGIN_SZ1362 1.8192252 0.1342208 13.554 < 2e-16 ***
ORIGIN_SZ1368 2.7645533 0.1285896 21.499 < 2e-16 ***
ORIGIN_SZ1369 2.6027035 0.1286049 20.238 < 2e-16 ***
ORIGIN_SZ1370 3.8036915 0.1284010 29.624 < 2e-16 ***
ORIGIN_SZ1371 3.1576240 0.1286811 24.538 < 2e-16 ***
ORIGIN_SZ1372 2.4538287 0.1289224 19.033 < 2e-16 ***
ORIGIN_SZ1373 0.6333383 0.1364235 4.642 3.44e-06 ***
ORIGIN_SZ1374 2.7384886 0.1288234 21.258 < 2e-16 ***
ORIGIN_SZ1375 4.2928205 0.1285257 33.400 < 2e-16 ***
ORIGIN_SZ1376 3.5917491 0.1289104 27.862 < 2e-16 ***
ORIGIN_SZ1379 1.7826380 0.1328203 13.421 < 2e-16 ***
ORIGIN_SZ1380 5.9283182 0.1283474 46.190 < 2e-16 ***
ORIGIN_SZ1381 5.4882843 0.1283667 42.755 < 2e-16 ***
ORIGIN_SZ1382 4.9117358 0.1284613 38.235 < 2e-16 ***
ORIGIN_SZ1383 2.5047943 0.1306096 19.178 < 2e-16 ***
ORIGIN_SZ1388 3.4254679 0.1284633 26.665 < 2e-16 ***
ORIGIN_SZ1389 2.4876666 0.1286256 19.340 < 2e-16 ***
ORIGIN_SZ1390 3.3067639 0.1284756 25.738 < 2e-16 ***
ORIGIN_SZ1391 3.2746314 0.1285167 25.480 < 2e-16 ***
ORIGIN_SZ1392 2.8425458 0.1293811 21.970 < 2e-16 ***
ORIGIN_SZ1393 2.0483419 0.1291043 15.866 < 2e-16 ***
ORIGIN_SZ1394 3.8051463 0.1284633 29.620 < 2e-16 ***
ORIGIN_SZ1395 3.5510811 0.1285136 27.632 < 2e-16 ***
ORIGIN_SZ1396 4.6180112 0.1284032 35.965 < 2e-16 ***
ORIGIN_SZ1397 4.6804762 0.1284120 36.449 < 2e-16 ***
ORIGIN_SZ1398 3.6425787 0.1287543 28.291 < 2e-16 ***
ORIGIN_SZ1400 4.6759075 0.1284756 36.395 < 2e-16 ***
ORIGIN_SZ1401 5.0477274 0.1283715 39.321 < 2e-16 ***
ORIGIN_SZ1402 5.1011623 0.1283864 39.733 < 2e-16 ***
ORIGIN_SZ1404 5.1579558 0.1291829 39.928 < 2e-16 ***
ORIGIN_SZ1410 4.0420432 0.1283783 31.485 < 2e-16 ***
ORIGIN_SZ1411 2.9443932 0.1285443 22.906 < 2e-16 ***
ORIGIN_SZ1412 3.2692589 0.1284557 25.450 < 2e-16 ***
ORIGIN_SZ1413 4.0506420 0.1284059 31.546 < 2e-16 ***
ORIGIN_SZ1414 3.4833687 0.1284556 27.117 < 2e-16 ***
ORIGIN_SZ1415 2.9922201 0.1286207 23.264 < 2e-16 ***
ORIGIN_SZ1416 3.6221805 0.1284861 28.191 < 2e-16 ***
ORIGIN_SZ1417 3.7745313 0.1284677 29.381 < 2e-16 ***
ORIGIN_SZ1418 4.5713200 0.1283965 35.603 < 2e-16 ***
ORIGIN_SZ1419 4.0776729 0.1284703 31.740 < 2e-16 ***
ORIGIN_SZ1422 5.1072716 0.1284094 39.773 < 2e-16 ***
ORIGIN_SZ1423 6.0174788 0.1283608 46.879 < 2e-16 ***
ORIGIN_SZ1430 3.7176173 0.1284346 28.946 < 2e-16 ***
ORIGIN_SZ1431 3.7837295 0.1283933 29.470 < 2e-16 ***
ORIGIN_SZ1432 3.8109774 0.1283933 29.682 < 2e-16 ***
ORIGIN_SZ1433 2.5503882 0.1292669 19.730 < 2e-16 ***
ORIGIN_SZ1434 4.0586775 0.1284137 31.606 < 2e-16 ***
ORIGIN_SZ1435 4.4171474 0.1283683 34.410 < 2e-16 ***
ORIGIN_SZ1436 1.3014336 0.1303414 9.985 < 2e-16 ***
ORIGIN_SZ1437 4.5953172 0.1283794 35.795 < 2e-16 ***
ORIGIN_SZ1438 5.0522959 0.1283502 39.363 < 2e-16 ***
ORIGIN_SZ1439 5.6837551 0.1283414 44.286 < 2e-16 ***
ORIGIN_SZ1440 2.1137319 0.1298160 16.283 < 2e-16 ***
ORIGIN_SZ1442 4.9311239 0.1284811 38.380 < 2e-16 ***
ORIGIN_SZ1443 6.0037112 0.1283659 46.770 < 2e-16 ***
ORIGIN_SZ1444 5.0405899 0.1285228 39.219 < 2e-16 ***
ORIGIN_SZ1452 2.8355710 0.1285343 22.061 < 2e-16 ***
ORIGIN_SZ1453 3.0191038 0.1285082 23.493 < 2e-16 ***
ORIGIN_SZ1454 2.0338914 0.1295590 15.699 < 2e-16 ***
ORIGIN_SZ1455 3.3886706 0.1285616 26.358 < 2e-16 ***
ORIGIN_SZ1456 3.8310384 0.1284343 29.829 < 2e-16 ***
ORIGIN_SZ1457 4.6346391 0.1283695 36.104 < 2e-16 ***
ORIGIN_SZ1458 4.9957835 0.1283567 38.921 < 2e-16 ***
ORIGIN_SZ1459 4.4130417 0.1283861 34.373 < 2e-16 ***
ORIGIN_SZ1460 3.6434791 0.1284600 28.363 < 2e-16 ***
ORIGIN_SZ1461 2.3045877 0.1293119 17.822 < 2e-16 ***
ORIGIN_SZ1464 6.3897458 0.1283588 49.780 < 2e-16 ***
ORIGIN_SZ1465 5.8661209 0.1283977 45.687 < 2e-16 ***
ORIGIN_SZ1472 1.3939828 0.1297329 10.745 < 2e-16 ***
ORIGIN_SZ1473 2.4448601 0.1286541 19.003 < 2e-16 ***
ORIGIN_SZ1474 3.5730525 0.1284087 27.826 < 2e-16 ***
ORIGIN_SZ1475 4.4491102 0.1283738 34.657 < 2e-16 ***
ORIGIN_SZ1476 3.8272335 0.1284468 29.796 < 2e-16 ***
ORIGIN_SZ1477 5.3285635 0.1283352 41.521 < 2e-16 ***
ORIGIN_SZ1478 3.6039267 0.1284577 28.055 < 2e-16 ***
ORIGIN_SZ1479 3.8448908 0.1284294 29.938 < 2e-16 ***
ORIGIN_SZ1480 5.6525484 0.1283348 44.045 < 2e-16 ***
ORIGIN_SZ1481 2.9830024 0.1286726 23.183 < 2e-16 ***
ORIGIN_SZ1482 3.2109390 0.1289469 24.901 < 2e-16 ***
ORIGIN_SZ1485 5.8356487 0.1284019 45.448 < 2e-16 ***
ORIGIN_SZ1494 2.6615197 0.1288441 20.657 < 2e-16 ***
ORIGIN_SZ1495 2.8544767 0.1285226 22.210 < 2e-16 ***
ORIGIN_SZ1496 3.9820085 0.1283819 31.017 < 2e-16 ***
ORIGIN_SZ1497 4.2639611 0.1284014 33.208 < 2e-16 ***
ORIGIN_SZ1498 4.5908749 0.1283666 35.764 < 2e-16 ***
ORIGIN_SZ1499 4.8132685 0.1283545 37.500 < 2e-16 ***
ORIGIN_SZ1500 4.6822831 0.1284116 36.463 < 2e-16 ***
ORIGIN_SZ1501 4.9692036 0.1283562 38.714 < 2e-16 ***
ORIGIN_SZ1502 4.4058222 0.1283888 34.316 < 2e-16 ***
ORIGIN_SZ1506 0.5179581 0.1570543 3.298 0.000974 ***
ORIGIN_SZ1515 1.7290382 0.1298954 13.311 < 2e-16 ***
ORIGIN_SZ1516 3.3466520 0.1284607 26.052 < 2e-16 ***
ORIGIN_SZ1517 3.6509048 0.1284673 28.419 < 2e-16 ***
ORIGIN_SZ1518 3.5568481 0.1284967 27.680 < 2e-16 ***
ORIGIN_SZ1519 4.8299234 0.1283913 37.619 < 2e-16 ***
ORIGIN_SZ1520 4.2751225 0.1283941 33.297 < 2e-16 ***
ORIGIN_SZ1521 2.7894687 0.1287420 21.667 < 2e-16 ***
ORIGIN_SZ1522 5.1661426 0.1283506 40.250 < 2e-16 ***
ORIGIN_SZ1523 3.7864551 0.1291094 29.327 < 2e-16 ***
ORIGIN_SZ1524 3.8500073 0.1286372 29.929 < 2e-16 ***
ORIGIN_SZ1527 3.7673049 0.1292927 29.138 < 2e-16 ***
ORIGIN_SZ1535 0.3888724 0.1550492 2.508 0.012140 *
ORIGIN_SZ1536 1.1053648 0.1318190 8.385 < 2e-16 ***
ORIGIN_SZ1537 1.8835853 0.1293558 14.561 < 2e-16 ***
ORIGIN_SZ1538 3.4387325 0.1284423 26.773 < 2e-16 ***
ORIGIN_SZ1539 3.9563792 0.1283960 30.814 < 2e-16 ***
ORIGIN_SZ1540 4.4721293 0.1283723 34.837 < 2e-16 ***
ORIGIN_SZ1541 5.7156003 0.1283961 44.515 < 2e-16 ***
ORIGIN_SZ1542 2.6724609 0.1290771 20.704 < 2e-16 ***
ORIGIN_SZ1543 3.4434117 0.1299502 26.498 < 2e-16 ***
ORIGIN_SZ1544 4.4318328 0.1284575 34.500 < 2e-16 ***
ORIGIN_SZ1547 1.3944409 0.1408842 9.898 < 2e-16 ***
ORIGIN_SZ1556 0.9903462 0.1420249 6.973 3.10e-12 ***
ORIGIN_SZ1557 1.1190759 0.1323181 8.457 < 2e-16 ***
ORIGIN_SZ1558 2.4026456 0.1294496 18.560 < 2e-16 ***
ORIGIN_SZ1559 4.1062899 0.1283844 31.984 < 2e-16 ***
ORIGIN_SZ1560 4.9133558 0.1283512 38.281 < 2e-16 ***
ORIGIN_SZ1561 4.7433747 0.1283807 36.948 < 2e-16 ***
ORIGIN_SZ1562 1.7916994 0.1297135 13.813 < 2e-16 ***
ORIGIN_SZ1563 3.6182330 0.1284897 28.160 < 2e-16 ***
ORIGIN_SZ1564 2.7474915 0.1289386 21.309 < 2e-16 ***
ORIGIN_SZ1565 2.8419407 0.1289732 22.035 < 2e-16 ***
ORIGIN_SZ1566 2.6220128 0.1296302 20.227 < 2e-16 ***
ORIGIN_SZ1567 0.4189659 0.1552622 2.698 0.006967 **
ORIGIN_SZ1568 1.4806010 0.1416837 10.450 < 2e-16 ***
ORIGIN_SZ1578 -1.3398701 0.2815434 -4.759 1.95e-06 ***
ORIGIN_SZ1580 2.5802806 0.1291851 19.974 < 2e-16 ***
ORIGIN_SZ1581 1.3677498 0.1296889 10.546 < 2e-16 ***
ORIGIN_SZ1582 4.6045623 0.1283575 35.873 < 2e-16 ***
ORIGIN_SZ1583 2.8642254 0.1297258 22.079 < 2e-16 ***
ORIGIN_SZ1584 3.1251714 0.1286746 24.287 < 2e-16 ***
ORIGIN_SZ1585 3.8128714 0.1285971 29.650 < 2e-16 ***
ORIGIN_SZ1586 2.6711806 0.1289518 20.715 < 2e-16 ***
ORIGIN_SZ1589 1.7206351 0.1334863 12.890 < 2e-16 ***
ORIGIN_SZ1590 1.2315089 0.1435987 8.576 < 2e-16 ***
ORIGIN_SZ1600 4.7154141 0.1286556 36.651 < 2e-16 ***
ORIGIN_SZ1601 3.1966313 0.1285004 24.876 < 2e-16 ***
ORIGIN_SZ1602 3.8706844 0.1284335 30.138 < 2e-16 ***
ORIGIN_SZ1603 4.8145991 0.1283601 37.509 < 2e-16 ***
ORIGIN_SZ1604 3.2985528 0.1285190 25.666 < 2e-16 ***
ORIGIN_SZ1605 4.6900271 0.1283685 36.536 < 2e-16 ***
ORIGIN_SZ1606 4.2115271 0.1286096 32.747 < 2e-16 ***
ORIGIN_SZ1607 3.4365748 0.1286286 26.717 < 2e-16 ***
ORIGIN_SZ1608 5.4794962 0.1283774 42.683 < 2e-16 ***
ORIGIN_SZ1609 5.3707537 0.1284173 41.823 < 2e-16 ***
ORIGIN_SZ1610 1.8098403 0.1416268 12.779 < 2e-16 ***
ORIGIN_SZ1622 3.2746454 0.1298294 25.223 < 2e-16 ***
ORIGIN_SZ1623 4.5686096 0.1283625 35.591 < 2e-16 ***
ORIGIN_SZ1624 3.3451251 0.1285342 26.025 < 2e-16 ***
ORIGIN_SZ1625 4.7448807 0.1283786 36.960 < 2e-16 ***
ORIGIN_SZ1626 5.4031403 0.1283445 42.099 < 2e-16 ***
ORIGIN_SZ1627 3.7636640 0.1284854 29.293 < 2e-16 ***
ORIGIN_SZ1628 5.5191293 0.1283478 43.001 < 2e-16 ***
ORIGIN_SZ1629 4.4870676 0.1284694 34.927 < 2e-16 ***
ORIGIN_SZ1630 4.5796065 0.1285216 35.633 < 2e-16 ***
ORIGIN_SZ1631 1.1315331 0.1389935 8.141 3.92e-16 ***
ORIGIN_SZ1642 2.1664333 0.1309212 16.548 < 2e-16 ***
ORIGIN_SZ1643 4.5066494 0.1283725 35.106 < 2e-16 ***
ORIGIN_SZ1644 2.2746032 0.1292608 17.597 < 2e-16 ***
ORIGIN_SZ1645 3.7832826 0.1284349 29.457 < 2e-16 ***
ORIGIN_SZ1646 3.5931982 0.1285792 27.945 < 2e-16 ***
ORIGIN_SZ1647 3.9788139 0.1284222 30.982 < 2e-16 ***
ORIGIN_SZ1648 4.5988103 0.1283876 35.820 < 2e-16 ***
ORIGIN_SZ1649 5.3718355 0.1283546 41.852 < 2e-16 ***
ORIGIN_SZ1650 5.4873773 0.1284050 42.735 < 2e-16 ***
ORIGIN_SZ1664 -0.5466103 0.1813269 -3.015 0.002574 **
ORIGIN_SZ1665 4.6877073 0.1283604 36.520 < 2e-16 ***
ORIGIN_SZ1666 3.4062823 0.1284771 26.513 < 2e-16 ***
ORIGIN_SZ1667 4.4232882 0.1286615 34.379 < 2e-16 ***
ORIGIN_SZ1668 4.5318630 0.1283819 35.300 < 2e-16 ***
ORIGIN_SZ1670 5.4088882 0.1283477 42.142 < 2e-16 ***
ORIGIN_SZ1671 6.0838254 0.1284023 47.381 < 2e-16 ***
ORIGIN_SZ1672 5.7049441 0.1284293 44.421 < 2e-16 ***
ORIGIN_SZ1684 3.7187181 0.1288702 28.856 < 2e-16 ***
ORIGIN_SZ1685 4.2555448 0.1284035 33.142 < 2e-16 ***
ORIGIN_SZ1686 4.1437766 0.1284031 32.272 < 2e-16 ***
ORIGIN_SZ1687 3.6993537 0.1285034 28.788 < 2e-16 ***
ORIGIN_SZ1688 3.2422176 0.1285630 25.219 < 2e-16 ***
ORIGIN_SZ1689 2.8871351 0.1288455 22.408 < 2e-16 ***
ORIGIN_SZ1690 4.2769664 0.1284599 33.294 < 2e-16 ***
ORIGIN_SZ1691 5.0966925 0.1283750 39.702 < 2e-16 ***
ORIGIN_SZ1692 4.6944612 0.1285417 36.521 < 2e-16 ***
ORIGIN_SZ1706 4.2405145 0.1284411 33.015 < 2e-16 ***
ORIGIN_SZ1707 4.1267925 0.1283945 32.141 < 2e-16 ***
ORIGIN_SZ1708 4.6515595 0.1283637 36.237 < 2e-16 ***
ORIGIN_SZ1709 3.7700021 0.1284598 29.348 < 2e-16 ***
ORIGIN_SZ1710 4.9670420 0.1283684 38.694 < 2e-16 ***
ORIGIN_SZ1711 4.7983231 0.1283920 37.372 < 2e-16 ***
ORIGIN_SZ1712 5.4136434 0.1283471 42.180 < 2e-16 ***
ORIGIN_SZ1713 3.0125277 0.1288959 23.372 < 2e-16 ***
ORIGIN_SZ1714 5.6442978 0.1283871 43.963 < 2e-16 ***
ORIGIN_SZ1727 4.4574547 0.1284012 34.715 < 2e-16 ***
ORIGIN_SZ1728 4.3351186 0.1283855 33.766 < 2e-16 ***
ORIGIN_SZ1729 3.7785773 0.1284218 29.423 < 2e-16 ***
ORIGIN_SZ1730 1.7369592 0.1300694 13.354 < 2e-16 ***
ORIGIN_SZ1731 4.6338734 0.1283936 36.091 < 2e-16 ***
ORIGIN_SZ1732 5.0905241 0.1283553 39.660 < 2e-16 ***
ORIGIN_SZ1733 4.8477092 0.1283778 37.761 < 2e-16 ***
ORIGIN_SZ1734 5.2568117 0.1283742 40.949 < 2e-16 ***
ORIGIN_SZ1735 6.9689832 0.1284616 54.250 < 2e-16 ***
ORIGIN_SZ1748 3.1734114 0.1286335 24.670 < 2e-16 ***
ORIGIN_SZ1749 4.1468003 0.1283953 32.297 < 2e-16 ***
ORIGIN_SZ1750 3.2613612 0.1284986 25.381 < 2e-16 ***
ORIGIN_SZ1751 2.5480666 0.1287617 19.789 < 2e-16 ***
ORIGIN_SZ1753 5.1283339 0.1283607 39.953 < 2e-16 ***
ORIGIN_SZ1754 5.5104972 0.1283459 42.935 < 2e-16 ***
ORIGIN_SZ1755 5.0221300 0.1283760 39.120 < 2e-16 ***
ORIGIN_SZ1756 4.9811190 0.1284102 38.791 < 2e-16 ***
ORIGIN_SZ1757 2.9497619 0.1319618 22.353 < 2e-16 ***
ORIGIN_SZ1769 3.9626587 0.1284323 30.854 < 2e-16 ***
ORIGIN_SZ1770 3.9969946 0.1285514 31.093 < 2e-16 ***
ORIGIN_SZ1771 2.7783443 0.1286934 21.589 < 2e-16 ***
ORIGIN_SZ1772 1.6643605 0.1304154 12.762 < 2e-16 ***
ORIGIN_SZ1774 4.8462943 0.1283722 37.752 < 2e-16 ***
ORIGIN_SZ1775 4.5115076 0.1284142 35.132 < 2e-16 ***
ORIGIN_SZ1776 5.7008216 0.1283497 44.416 < 2e-16 ***
ORIGIN_SZ1777 5.7202295 0.1283656 44.562 < 2e-16 ***
ORIGIN_SZ1778 5.5268171 0.1288405 42.897 < 2e-16 ***
ORIGIN_SZ1790 4.6407250 0.1283929 36.145 < 2e-16 ***
ORIGIN_SZ1791 4.0003425 0.1284480 31.144 < 2e-16 ***
ORIGIN_SZ1792 3.9251321 0.1284655 30.554 < 2e-16 ***
ORIGIN_SZ1793 2.0307331 0.1289694 15.746 < 2e-16 ***
ORIGIN_SZ1794 1.7992380 0.1310605 13.728 < 2e-16 ***
ORIGIN_SZ1795 1.3069606 0.1322365 9.884 < 2e-16 ***
ORIGIN_SZ1796 5.3162956 0.1283742 41.412 < 2e-16 ***
ORIGIN_SZ1797 5.3447045 0.1283626 41.638 < 2e-16 ***
ORIGIN_SZ1798 5.3785600 0.1283640 41.901 < 2e-16 ***
ORIGIN_SZ1799 4.6072423 0.1285228 35.848 < 2e-16 ***
ORIGIN_SZ1800 3.9498043 0.1308451 30.187 < 2e-16 ***
ORIGIN_SZ1811 3.7138890 0.1284970 28.903 < 2e-16 ***
ORIGIN_SZ1812 4.8789898 0.1283529 38.012 < 2e-16 ***
ORIGIN_SZ1813 4.6561018 0.1283626 36.273 < 2e-16 ***
ORIGIN_SZ1817 5.4056473 0.1283943 42.102 < 2e-16 ***
ORIGIN_SZ1818 5.1927141 0.1283798 40.448 < 2e-16 ***
ORIGIN_SZ1819 5.7273655 0.1283578 44.620 < 2e-16 ***
ORIGIN_SZ1820 2.8647670 0.1327721 21.577 < 2e-16 ***
ORIGIN_SZ1832 4.5074899 0.1284059 35.103 < 2e-16 ***
ORIGIN_SZ1833 3.9377954 0.1284330 30.660 < 2e-16 ***
ORIGIN_SZ1834 4.2644257 0.1283825 33.217 < 2e-16 ***
ORIGIN_SZ1835 3.5659499 0.1285070 27.749 < 2e-16 ***
ORIGIN_SZ1837 0.7690953 0.1419186 5.419 5.98e-08 ***
ORIGIN_SZ1839 4.6358637 0.1284983 36.077 < 2e-16 ***
ORIGIN_SZ1840 6.4716119 0.1283366 50.427 < 2e-16 ***
ORIGIN_SZ1841 2.2983709 0.1330375 17.276 < 2e-16 ***
ORIGIN_SZ1842 6.4694885 0.1287331 50.255 < 2e-16 ***
ORIGIN_SZ1853 4.3256678 0.1283955 33.690 < 2e-16 ***
ORIGIN_SZ1854 4.5606620 0.1283856 35.523 < 2e-16 ***
ORIGIN_SZ1855 4.8503696 0.1283699 37.784 < 2e-16 ***
ORIGIN_SZ1858 2.6470639 0.1307361 20.247 < 2e-16 ***
ORIGIN_SZ1860 5.9892312 0.1285733 46.582 < 2e-16 ***
ORIGIN_SZ1861 5.4449058 0.1283857 42.411 < 2e-16 ***
ORIGIN_SZ1874 4.5098276 0.1284380 35.113 < 2e-16 ***
ORIGIN_SZ1875 2.8330493 0.1289053 21.978 < 2e-16 ***
ORIGIN_SZ1876 4.9442722 0.1287017 38.417 < 2e-16 ***
ORIGIN_SZ1877 4.5626564 0.1283895 35.538 < 2e-16 ***
ORIGIN_SZ1880 0.9829313 0.1365106 7.200 6.00e-13 ***
ORIGIN_SZ1882 5.2992540 0.1283965 41.273 < 2e-16 ***
ORIGIN_SZ1883 5.8024625 0.1285970 45.121 < 2e-16 ***
ORIGIN_SZ1895 4.6351599 0.1283881 36.103 < 2e-16 ***
ORIGIN_SZ1896 2.9955843 0.1286416 23.286 < 2e-16 ***
ORIGIN_SZ1897 3.6604153 0.1285855 28.467 < 2e-16 ***
ORIGIN_SZ1898 -0.6599083 0.1778219 -3.711 0.000206 ***
ORIGIN_SZ1901 0.7749620 0.1467246 5.282 1.28e-07 ***
ORIGIN_SZ1903 5.1887292 0.1285909 40.351 < 2e-16 ***
ORIGIN_SZ1917 3.2192269 0.1286185 25.029 < 2e-16 ***
ORIGIN_SZ1918 4.6602616 0.1284272 36.287 < 2e-16 ***
ORIGIN_SZ1919 4.5380961 0.1284026 35.343 < 2e-16 ***
ORIGIN_SZ1922 2.3087644 0.1312319 17.593 < 2e-16 ***
ORIGIN_SZ1924 5.0214296 0.1286230 39.040 < 2e-16 ***
ORIGIN_SZ1937 4.0309239 0.1284751 31.375 < 2e-16 ***
ORIGIN_SZ1938 4.6755113 0.1283771 36.420 < 2e-16 ***
ORIGIN_SZ1939 5.2285909 0.1283681 40.731 < 2e-16 ***
ORIGIN_SZ1942 1.2796556 0.1345281 9.512 < 2e-16 ***
ORIGIN_SZ1959 3.6051332 0.1285704 28.040 < 2e-16 ***
ORIGIN_SZ1960 5.5903041 0.1283372 43.559 < 2e-16 ***
ORIGIN_SZ1961 3.9886969 0.1284784 31.046 < 2e-16 ***
ORIGIN_SZ1962 5.0143993 0.1283745 39.061 < 2e-16 ***
ORIGIN_SZ1964 0.2513609 0.1525944 1.647 0.099507 .
ORIGIN_SZ1979 3.9080186 0.1285324 30.405 < 2e-16 ***
ORIGIN_SZ1980 2.1544333 0.1290272 16.698 < 2e-16 ***
ORIGIN_SZ1981 4.6365812 0.1283758 36.117 < 2e-16 ***
ORIGIN_SZ1982 3.4508601 0.1287496 26.803 < 2e-16 ***
ORIGIN_SZ1983 4.9242564 0.1283778 38.358 < 2e-16 ***
ORIGIN_SZ1984 3.6431087 0.1285296 28.345 < 2e-16 ***
ORIGIN_SZ1985 4.4345906 0.1284509 34.524 < 2e-16 ***
ORIGIN_SZ2001 4.2184167 0.1284302 32.846 < 2e-16 ***
ORIGIN_SZ2002 4.7630499 0.1283596 37.107 < 2e-16 ***
ORIGIN_SZ2003 4.3973471 0.1283983 34.248 < 2e-16 ***
ORIGIN_SZ2004 5.0199149 0.1283720 39.104 < 2e-16 ***
ORIGIN_SZ2005 4.8956048 0.1283712 38.136 < 2e-16 ***
ORIGIN_SZ2006 3.4575991 0.1286229 26.882 < 2e-16 ***
ORIGIN_SZ2007 2.8498303 0.1292845 22.043 < 2e-16 ***
ORIGIN_SZ2022 4.5952513 0.1284300 35.780 < 2e-16 ***
ORIGIN_SZ2023 5.0117105 0.1283577 39.045 < 2e-16 ***
ORIGIN_SZ2024 4.3242920 0.1283898 33.681 < 2e-16 ***
ORIGIN_SZ2025 4.3546802 0.1283861 33.919 < 2e-16 ***
ORIGIN_SZ2026 3.0208249 0.1287979 23.454 < 2e-16 ***
ORIGIN_SZ2027 5.3158698 0.1283666 41.412 < 2e-16 ***
ORIGIN_SZ2043 3.9075284 0.1285194 30.404 < 2e-16 ***
ORIGIN_SZ2044 4.6274993 0.1283729 36.047 < 2e-16 ***
ORIGIN_SZ2045 0.3537318 0.1435921 2.463 0.013761 *
ORIGIN_SZ2046 4.5807504 0.1283630 35.686 < 2e-16 ***
ORIGIN_SZ2047 4.3432419 0.1284089 33.824 < 2e-16 ***
ORIGIN_SZ2048 4.6367218 0.1283862 36.115 < 2e-16 ***
ORIGIN_SZ2049 3.7174760 0.1289577 28.827 < 2e-16 ***
ORIGIN_SZ2064 4.5752841 0.1283961 35.634 < 2e-16 ***
ORIGIN_SZ2065 3.0666127 0.1285674 23.852 < 2e-16 ***
ORIGIN_SZ2066 2.4252096 0.1303253 18.609 < 2e-16 ***
ORIGIN_SZ2067 5.8329188 0.1283346 45.451 < 2e-16 ***
ORIGIN_SZ2068 4.1693543 0.1284817 32.451 < 2e-16 ***
ORIGIN_SZ2069 4.5189874 0.1284176 35.190 < 2e-16 ***
ORIGIN_SZ2085 3.4872368 0.1286312 27.110 < 2e-16 ***
ORIGIN_SZ2086 4.9165833 0.1283673 38.301 < 2e-16 ***
ORIGIN_SZ2087 3.5650820 0.1284901 27.746 < 2e-16 ***
ORIGIN_SZ2088 4.2418364 0.1283844 33.040 < 2e-16 ***
ORIGIN_SZ2089 3.9807971 0.1284591 30.989 < 2e-16 ***
ORIGIN_SZ2090 5.5293310 0.1283511 43.080 < 2e-16 ***
ORIGIN_SZ2091 0.9136463 0.1430196 6.388 1.68e-10 ***
ORIGIN_SZ2105 1.6527954 0.1617990 10.215 < 2e-16 ***
ORIGIN_SZ2106 1.8173872 0.1296309 14.020 < 2e-16 ***
ORIGIN_SZ2107 3.0072150 0.1285965 23.385 < 2e-16 ***
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DESTIN_SZ2150 -1.0887767 0.0518064 -21.016 < 2e-16 ***
DESTIN_SZ2151 0.5962899 0.0512590 11.633 < 2e-16 ***
DESTIN_SZ2152 -0.3742242 0.0514138 -7.279 3.37e-13 ***
DESTIN_SZ2153 -1.6780871 0.0523817 -32.036 < 2e-16 ***
DESTIN_SZ2171 -0.1744648 0.0514510 -3.391 0.000697 ***
DESTIN_SZ2172 -1.8376704 0.0523240 -35.121 < 2e-16 ***
DESTIN_SZ2173 -1.4517682 0.0516775 -28.093 < 2e-16 ***
DESTIN_SZ2174 -0.7973274 0.0515841 -15.457 < 2e-16 ***
DESTIN_SZ2191 0.0902737 0.0516998 1.746 0.080791 .
DESTIN_SZ2192 -1.2790689 0.0522786 -24.466 < 2e-16 ***
DESTIN_SZ2193 -0.6378899 0.0515557 -12.373 < 2e-16 ***
DESTIN_SZ2194 -0.6737004 0.0514791 -13.087 < 2e-16 ***
DESTIN_SZ2195 -2.5995678 0.0623353 -41.703 < 2e-16 ***
DESTIN_SZ2212 0.0746680 0.0528250 1.413 0.157510
DESTIN_SZ2213 -0.2507887 0.0518153 -4.840 1.30e-06 ***
DESTIN_SZ2214 0.4079463 0.0517061 7.890 3.03e-15 ***
DESTIN_SZ2215 -1.2526124 0.0520350 -24.072 < 2e-16 ***
DESTIN_SZ2216 -0.4016979 0.0515234 -7.796 6.37e-15 ***
DESTIN_SZ2233 0.4360380 0.0521165 8.367 < 2e-16 ***
DESTIN_SZ2234 0.9816535 0.0518510 18.932 < 2e-16 ***
DESTIN_SZ2235 -0.3711216 0.0519384 -7.145 8.97e-13 ***
DESTIN_SZ2236 -1.8616497 0.0529479 -35.160 < 2e-16 ***
DESTIN_SZ2237 -0.3613258 0.0524631 -6.887 5.69e-12 ***
DESTIN_SZ2256 -0.1486757 0.0526155 -2.826 0.004718 **
DESTIN_SZ2257 -2.6465337 0.0575364 -45.998 < 2e-16 ***
DESTIN_SZ2258 -0.6302004 0.0516952 -12.191 < 2e-16 ***
DESTIN_SZ2259 0.4493450 0.0522187 8.605 < 2e-16 ***
DESTIN_SZ2277 -1.4277992 0.0572798 -24.927 < 2e-16 ***
DESTIN_SZ2278 -1.0987939 0.0535642 -20.514 < 2e-16 ***
DESTIN_SZ2279 -0.4217723 0.0517179 -8.155 3.48e-16 ***
DESTIN_SZ2280 -1.6980359 0.0600373 -28.283 < 2e-16 ***
DESTIN_SZ2297 -1.6317059 0.0544077 -29.990 < 2e-16 ***
DESTIN_SZ2300 -1.5357290 0.0551923 -27.825 < 2e-16 ***
DESTIN_SZ2301 -0.7032192 0.0521112 -13.495 < 2e-16 ***
DESTIN_SZ2318 0.7165873 0.0514743 13.921 < 2e-16 ***
DESTIN_SZ2319 0.7156622 0.0514403 13.912 < 2e-16 ***
DESTIN_SZ2322 -0.2356355 0.0519697 -4.534 5.79e-06 ***
DESTIN_SZ2337 0.2733136 0.0544478 5.020 5.17e-07 ***
DESTIN_SZ2341 1.0100202 0.0514164 19.644 < 2e-16 ***
DESTIN_SZ2343 -1.1431043 0.0527584 -21.667 < 2e-16 ***
DESTIN_SZ2361 -0.3581483 0.0520025 -6.887 5.69e-12 ***
DESTIN_SZ2364 -2.2471011 0.0591155 -38.012 < 2e-16 ***
DESTIN_SZ2379 -1.2051440 0.0579292 -20.804 < 2e-16 ***
DESTIN_SZ2384 0.7246833 0.0515972 14.045 < 2e-16 ***
DESTIN_SZ2405 1.3975678 0.0514186 27.180 < 2e-16 ***
DESTIN_SZ2406 -1.6290299 0.0563539 -28.907 < 2e-16 ***
DESTIN_SZ2426 0.8495482 0.0523702 16.222 < 2e-16 ***
DESTIN_SZ2427 1.1361526 0.0516163 22.012 < 2e-16 ***
DESTIN_SZ2505 0.7094831 0.0546883 12.973 < 2e-16 ***
log(dist) -1.6146098 0.0002885 -5595.605 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for poisson family taken to be 1)
Null deviance: 101244825 on 64961 degrees of freedom
Residual deviance: 25322395 on 63326 degrees of freedom
AIC: 25684037
Number of Fisher Scoring iterations: 10In the Destin Constrained Model, the coefficients for five variables are all NA (Not Available), meaning that suitable coefficient values could not be calculated during the model fitting process. The specific cause requires further examination
For the purpose of model comparison, we decided to exclude Destin Constrained Model. This ensures that, for a reliable comparison of model performance, the comparison is based on reliable estimates, avoiding the influence of variables with coefficients that could not be computed.
9 Model Comparison
First of all, let us create a list called model_list by using the code chunk below. It contains all our fitted models for all four variations of gravity model.
model_list <- list(
Unconstrained = uncSIM,
Origin_Constrained = orcSIM,
Doubly_Constrained = dbcSIM)Next, we will compute the RMSE of all the models in model_list file by using the code chunk below.
The RMSE values provide a measure of the goodness of fit for each model. A lower RMSE indicates better model performance in terms of how well the model predictions align with the observed values. In this comparison, the Doubly Constrained Model has the lowest RMSE (1219.291), suggesting that it performs better in terms of minimizing prediction errors compared to the Unconstrained and Origin Constrained models.
compare_performance(model_list,
metrics = "RMSE")# Comparison of Model Performance Indices
Name | Model | RMSE
-------------------------------------
Unconstrained | glm | 1773.898
Origin_Constrained | glm | 1653.729
Doubly_Constrained | glm | 1219.2919.1 Visualising the fitted values
We will do a plot to visualise the observed values and the fitted values.
Firstly we will extract the fitted values from each model by using the code chunk below.
df <- as.data.frame(uncSIM$fitted.values) %>%
round(digits = 0)Next, we will join the values to SIM_data data frame:
inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(uncTRIPS = "uncSIM$fitted.values")Repeat the same step by for Origin Constrained SIM:
df <- as.data.frame(orcSIM$fitted.values) %>%
round(digits = 0)inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(orcTRIPS = "orcSIM$fitted.values")Repeat the same step by for Doubly Constrained SIM:
df<- as.data.frame(dbcSIM$fitted.values) %>%
round(digits = 0)inter_zonal_flow <- inter_zonal_flow %>%
cbind(df) %>%
rename(dbcTRIPS = "dbcSIM$fitted.values")We will create scatter plots displaying the relationship between actual and predicted values through linear fitting and compare each other.
Code
unc_p <- ggplot(data = inter_zonal_flow,
aes(x = uncTRIPS,
y = MORNING_PEAK)) +
geom_point(color = "darkgreen") +
geom_smooth(method = lm, color = "yellow") +
theme_minimal()
coord_cartesian(xlim=c(0,100000),
ylim=c(0,100000))<ggproto object: Class CoordCartesian, Coord, gg>
aspect: function
backtransform_range: function
clip: on
default: FALSE
distance: function
expand: TRUE
is_free: function
is_linear: function
labels: function
limits: list
modify_scales: function
range: function
render_axis_h: function
render_axis_v: function
render_bg: function
render_fg: function
setup_data: function
setup_layout: function
setup_panel_guides: function
setup_panel_params: function
setup_params: function
train_panel_guides: function
transform: function
super: <ggproto object: Class CoordCartesian, Coord, gg>Code
orc_p <- ggplot(data = inter_zonal_flow,
aes(x = orcTRIPS,
y = MORNING_PEAK)) +
geom_point(color = "darkgreen") +
geom_smooth(method = lm, color = "yellow") +
theme_minimal()+
coord_cartesian(xlim=c(0,100000),
ylim=c(0,100000))
dbc_p <- ggplot(data = inter_zonal_flow,
aes(x = dbcTRIPS,
y = MORNING_PEAK)) +
geom_point(color = "darkgreen") +
geom_smooth(method = lm, color = "yellow") +
theme_minimal()+
coord_cartesian(xlim=c(0,100000),
ylim=c(0,100000))
ggarrange( unc_p, orc_p, dbc_p,
ncol = 2,
nrow = 2)
The results indicate that for the Doubly Constrained Model, the scatter plot points closely follow the fitted curve. This tight distribution suggests strong linear correlation between the actual values and the model predictions. The model appears to accurately capture the variation trends in the actual values, making it well-suited for describing underlying relationships.
10 Conclusion
In the comparison of three spatial interaction models (UNC, ORC, DBC), insights are provided through the examination of R-squared values. Specifically, the DBC model stands out with an R-squared value of 59%, signifying superior explanatory power among the considered models. Additionally, the comparison of Root Mean Square Error (RMSE) reveals that the DBC model has the lowest RMSE at 1219.291. This implies that the DBC model demonstrates the least average deviation in predictions compared to observed values, showcasing higher predictive accuracy.
According to the UNC and ORC models, the p-values of all the variables are very small (<0.05) , indicating that their contributions in the models are highly statistically significant. Considering both models, Entertainment consistently emerges as the variable with the most significant positive impact, followed by School and HDB. Distance consistently exhibits the most significant negative impact in both the UNC and ORC models.